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Моделирование процесса коагуляции в криволинейном потоке в масляных системах судовых энергетических установок..pdf

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ǝǟǐǚǎǧǑǩǙǑǜǏǑǞǔǣǑǝǖǔǑǟǝǞnjǙǚǎǖǔ
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ɩɨɥɟɫɩɨɫɨɛɫɬɜɭɟɬɩɪɨɰɟɫɫɭɮɥɨɤɭɥɨɨɛɪɚɡɨɜɚɧɢɹɱɬɨɜɫɜɨɸɨɱɟɪɟɞɶɭɜɟɥɢɱɢɜɚɟɬɰɟɧɬɪɨɛɟɠɧɭɸɫɢɥɭɜ
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Выпуск 2
ȼɜɟɞɟɧɢɟ
ȼɫɬɚɬɶɟɩɪɢɜɟɞɟɧɚɦɚɬɟɦɚɬɢɱɟɫɤɚɹɦɨɞɟɥɶɤɨɚɝɭɥɹɰɢɢɞɜɭɯɱɚɫɬɢɰɜɪɚɛɨɱɟɣɡɨɧɟɝɢɞɪɨ
ɰɢɤɥɨɧɨɜɫɪɚɞɢɚɥɶɧɵɦɦɚɝɧɢɬɧɵɦɩɨɥɟɦɜɵɩɨɥɧɟɧɧɚɹɜɰɢɥɢɧɞɪɢɱɟɫɤɨɣɫɢɫɬɟɦɟɤɨɨɪɞɢɧɚɬ
ɇɟɫɦɨɬɪɹɧɚɬɨɱɬɨɰɢɤɥɨɧɵɢɝɢɞɪɨɰɢɤɥɨɧɵɢɫɩɨɥɶɡɭɸɬɫɹɩɨɜɫɟɦɟɫɬɧɨɜɧɚɫɬɨɹɳɟɟɜɪɟɦɹɧɟ
ɫɭɳɟɫɬɜɭɟɬɩɪɢɟɦɥɟɦɨɣɢɬɨɱɧɨɣɦɨɞɟɥɢɤɢɧɟɬɢɤɢɱɚɫɬɢɰɜɤɪɢɜɨɥɢɧɟɣɧɨɦɩɨɬɨɤɟ
Ⱥɧɚɥɢɡɫɨɜɪɟɦɟɧɧɵɯɫɭɞɨɜɵɯɷɧɟɪɝɟɬɢɱɟɫɤɢɯɭɫɬɚɧɨɜɨɤɩɨɤɚɡɵɜɚɟɬɱɬɨɜɨɩɪɨɫɵɫɜɹɡɚɧ
ɧɵɟɫɩɨɜɵɲɟɧɢɟɦɷɮɮɟɤɬɢɜɧɨɫɬɢɞɜɢɝɚɬɟɥɟɣɜɧɭɬɪɟɧɧɟɝɨɫɝɨɪɚɧɢɹȾȼɋɞɨɫɢɯɩɨɪɚɤɬɭɚɥɶɧɵ
Ɉɫɧɨɜɧɵɦɬɢɩɨɦɞɜɢɝɚɬɟɥɹɧɚɜɫɟɯɫɨɜɪɟɦɟɧɧɵɯɫɭɞɚɯɤɚɤɪɟɱɧɨɝɨɬɚɤɢɦɨɪɫɤɨɝɨɮɥɨɬɚɹɜɥɹɟɬ
ɫɹȾȼɋɩɪɢɷɬɨɦɝɨɞɨɜɵɟɪɚɫɯɨɞɵɧɚɝɨɪɸɱɟɫɦɚɡɨɱɧɵɟɦɚɬɟɪɢɚɥɵɦɨɝɭɬɩɪɟɜɵɲɚɬɶɫɬɨɢɦɨɫɬɶ
127
Выпуск 2
ɫɚɦɨɝɨɞɢɡɟɥɹɜɧɟɫɤɨɥɶɤɨɪɚɡȼɫɜɹɡɢɫɬɟɦɱɬɨɩɨɬɟɪɢɦɨɳɧɨɫɬɢɧɚɢɡɧɨɫɩɪɢɧɟɩɪɚɜɢɥɶɧɨɣ
ɷɤɫɩɥɭɚɬɚɰɢɢ ɫɨɫɬɚɜɥɹɸɬ ɜ ɫɪɟɞɧɟɦ ± ɩɪɨɰɟɫɫ ɪɟɝɟɧɟɪɚɰɢɢ ɦɚɫɟɥ ɹɜɥɹɟɬɫɹ ɨɞɧɢɦ ɢɡ
ɜɚɠɧɟɣɲɢɯɢɧɟɨɬɥɨɠɧɵɯɧɚɜɨɞɧɨɦɬɪɚɧɫɩɨɪɬɟɩɨɫɤɨɥɶɤɭɟɫɥɢɜɨɜɪɟɦɹɧɟɜɵɩɨɥɧɢɬɶɡɚɦɟɧɭ
ɦɨɬɨɪɧɨɝɨɦɚɫɥɚɬɨɢɡɧɨɫȾȼɋɭɜɟɥɢɱɢɬɫɹɧɚ±>@
ɋɭɳɟɫɬɜɭɸɬ ɱɟɬɵɪɟ ɛɚɡɨɜɵɯ ɦɟɬɨɞɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɨɱɢɫɬɤɢ ɬɟɯɧɢɱɟɫɤɢɯ ɠɢɞɤɨɫɬɟɣ ɝɪɚ
ɜɢɬɚɰɢɨɧɧɵɣ ɢɧɟɪɰɢɨɧɧɵɣ ɫɢɬɨɜɵɣ ɢ ɫɟɩɚɪɚɰɢɨɧɧɵɣ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ ɜɨɡɞɟɣɫɬɜɢɹ
ȼ ɫɜɹɡɢɫɬɟɦɱɬɨɧɚɢɛɨɥɟɟɨɩɚɫɧɵɦɢɩɪɢɦɟɫɹɦɢɜɦɨɬɨɪɧɨɦɦɚɫɥɟɜɵɫɬɭɩɚɸɬɩɪɨɞɭɤɬɵɢɡɧɨɫɚ
ɤɨɬɨɪɵɟɩɨɫɜɨɟɣɩɪɢɪɨɞɟɹɜɥɹɸɬɫɹɮɟɪɪɨɦɚɝɧɢɬɧɵɦɢɷɮɮɟɤɬɢɜɧɨɫɬɶɨɱɢɫɬɤɢɠɟɥɟɡɨɫɨɞɟɪɠɚ
ɳɢɯɞɢɫɩɟɪɫɧɵɯɫɪɟɞɦɨɠɟɬɢɧɬɟɧɫɢɮɢɰɢɪɨɜɚɬɶɫɹɩɭɬɟɦɧɚɥɨɠɟɧɢɹɦɚɝɧɢɬɧɨɝɨɩɨɥɹɧɚɢɡɜɟɫɬ
ɧɵɟɭɫɬɪɨɣɫɬɜɚ>@
Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɪɢɦɟɫɢ ɛɨɥɶɲɨɝɨ ɪɚɡɦɟɪɚ ɜ ɧɟɨɱɢɳɟɧɧɨɣ ɜɹɡɤɨɣ ɫɪɟɞɟ ɥɟɝɤɨ ɭɞɚɥɹɸɬɫɹ
ɫɩɨɦɨɳɶɸɢɡɜɟɫɬɧɵɯɦɟɬɨɞɨɜɨɱɢɫɬɤɢɈɞɧɚɤɨɛɨɥɶɲɚɹɱɚɫɬɶɩɪɢɦɟɫɟɣɹɜɥɹɟɬɫɹɦɟɥɤɢɦɢɞɢɫ
ɩɟɪɫɧɵɦɢɱɚɫɬɢɰɚɦɢɤɨɬɨɪɵɟɜɜɢɞɭɦɚɥɨɝɨɪɚɡɦɟɪɚɩɥɨɯɨɩɨɞɞɚɸɬɫɹɢɡɜɥɟɱɟɧɢɸɬɪɚɞɢɰɢɨɧɧɵ
ɦɢɫɩɨɫɨɛɚɦɢ>@ɉɨɷɬɨɦɭɜɨɡɧɢɤɥɚɧɟɨɛɯɨɞɢɦɨɫɬɶɩɪɢɦɟɧɹɬɶɫɩɟɰɢɚɥɶɧɵɟɢɥɢɤɨɦɛɢɧɢɪɨɜɚɧ
ɧɵɟɦɟɬɨɞɵɨɱɢɫɬɤɢɈɞɧɢɦɢɡɧɚɢɛɨɥɟɟɩɟɪɫɩɟɤɬɢɜɧɵɯɹɜɥɹɟɬɫɹɧɚɥɨɠɟɧɢɟɩɨɥɟɣɷɥɟɤɬɪɢɱɟɫɤɨɣ
ɩɪɢɪɨɞɵɝɞɟɤɨɚɝɭɥɹɰɢɹɜɡɧɚɱɢɬɟɥɶɧɨɣɫɬɟɩɟɧɢɩɨɜɵɲɚɟɬɷɮɮɟɤɬɢɜɧɨɫɬɶɨɱɢɫɬɤɢ
Ʉɨɚɝɭɥɹɰɢɹ²ɩɪɨɰɟɫɫɨɛɴɟɞɢɧɟɧɢɹɦɟɥɤɢɯɱɚɫɬɢɰ ɜɛɨɥɟɟɤɪɭɩɧɵɟɩɨɞɞɟɣɫɬɜɢɟɦɫɢɥɫɰɟɩɥɟɧɢɹɆɚɥɟɧɶɤɢɟɱɚɫɬɢɰɵɨɛɴɟɞɢɧɹɸɬɫɹɜɛɨɥɶɲɢɟɚɝɥɨɦɟɪɚɬɵɧɚɡɵɜɚɟɦɵɟɮɥɨɤɭɥɚɦɢɤɨɬɨ
ɪɵɟɦɨɠɧɨɡɧɚɱɢɬɟɥɶɧɨɥɟɝɱɟɢɡɜɥɟɱɶɢɡɜɹɡɤɢɯɫɪɟɞ
ȼɤɚɱɟɫɬɜɟɩɪɢɦɟɪɚɭɫɩɟɲɧɨɝɨɩɪɢɦɟɧɟɧɢɹɦɚɝɧɢɬɧɵɯɩɨɥɟɣɫɬɪɚɞɢɰɢɨɧɧɵɦɢɦɟɬɨɞɚ
ɦɢɨɱɢɫɬɤɢɦɨɠɟɬɫɥɭɠɢɬɶɦɚɝɧɢɬɧɵɣɝɢɞɪɨɰɢɤɥɨɧɋɭɳɟɫɬɜɭɸɬɪɚɡɥɢɱɧɵɟɤɨɧɫɬɪɭɤɰɢɢɷɬɢɯ
ɚɩɩɚɪɚɬɨɜɨɞɧɚɤɨɧɚɢɛɨɥɶɲɭɸɩɨɩɭɥɹɪɧɨɫɬɶɩɨɥɭɱɢɥɝɢɞɪɨɰɢɤɥɨɧɫɪɚɞɢɚɥɶɧɵɦɦɚɝɧɢɬɧɵɦ
ɩɨɥɟɦɩɪɢɜɟɞɟɧɧɵɣɧɚɪɢɫɫɩɪɢɧɰɢɩɨɦɞɟɣɫɬɜɢɹɢɤɨɧɫɬɪɭɤɰɢɟɣɤɨɬɨɪɨɝɨɩɨɞɪɨɛɧɨɦɨɠɧɨ
ɨɡɧɚɤɨɦɢɬɶɫɹɜ>@
ɊɢɫȽɢɞɪɨɰɢɤɥɨɧɫɪɚɞɢɚɥɶɧɵɦɦɚɝɧɢɬɧɵɦɩɨɥɟɦ
128
Ⱦɢɧɚɦɢɤɟɱɚɫɬɢɰɜɪɚɛɨɱɟɣɤɚɦɟɪɟɰɢɤɥɨɧɨɜɢɝɢɞɪɨɰɢɤɥɨɧɨɜɩɨɫɜɹɳɟɧɪɹɞɢɫɫɥɟɞɨɜɚɧɢɣ
ɍɫɩɟɯɢɜɨɛɥɚɫɬɢɦɨɞɟɥɢɪɨɜɚɧɢɹɞɜɢɠɟɧɢɹɫɩɥɨɲɧɨɣɫɪɟɞɵɧɟɨɫɩɨɪɢɦɵɛɟɡɧɚɥɨɠɟɧɢɹɦɚɝɧɢɬ
ɧɨɝɨɩɨɥɹ>@±>@Ɉɞɧɚɤɨɩɪɨɰɟɫɫɤɨɚɝɭɥɹɰɢɢɢɥɢɩɨɥɧɨɫɬɶɸɨɬɫɭɬɫɬɜɭɟɬɢɥɢɧɨɫɢɬɷɦɩɢɪɢɱɟ
ɫɤɢɣɯɚɪɚɤɬɟɪɢɨɩɪɟɞɟɥɹɟɬɫɹɫɩɨɦɨɳɶɸɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɧɚɣɞɟɧɧɵɯɩɨɩɪɚɜɨɱɧɵɯɤɨɷɮɮɢɰɢ
ɟɧɬɨɜɩɪɢɦɟɧɢɬɶɤɨɬɨɪɵɟɦɨɠɧɨɬɨɥɶɤɨɤɤɨɧɤɪɟɬɧɵɦɚɩɩɚɪɚɬɚɦɊɚɧɟɟɛɵɥɚɪɚɡɪɚɛɨɬɚɧɚɦɨɞɟɥɶ
ɤɨɚɝɭɥɹɰɢɢɞɜɭɯɱɚɫɬɢɰɜɤɪɢɜɨɥɢɧɟɣɧɨɦɩɨɬɨɤɟɜɵɩɨɥɧɟɧɧɚɹɜɩɨɥɹɪɧɵɯɤɨɨɪɞɢɧɚɬɚɯɨɞɧɚɤɨ
ɢɨɧɚɬɪɟɛɭɟɬɞɚɥɶɧɟɣɲɟɝɨɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ>@Ɍɚɤɤɚɤɩɪɨɰɟɫɫɫɟɩɚɪɚɰɢɢɜɪɚɛɨɱɟɣɤɚɦɟɪɟ
ɝɢɞɪɨɰɢɤɥɨɧɚɹɜɥɹɟɬɫɹɫɥɨɠɧɵɦɢɧɟɩɨɞɞɚɟɬɫɹɩɨɥɧɨɫɬɶɸɚɧɚɥɢɬɢɱɟɫɤɨɦɭɢɥɢɬɟɨɪɟɬɢɱɟɫɤɨɦɭ
ɪɟɲɟɧɢɸɩɪɢɛɟɝɧɟɦɤɧɟɤɨɬɨɪɵɦɞɨɩɭɳɟɧɢɹɦɚɧɚɥɨɝɢɱɧɨɢɡɥɨɠɟɧɧɵɦɜ>@
±ɩɪɨɰɟɫɫɹɜɥɹɟɬɫɹɭɫɬɚɧɨɜɢɜɲɢɦɫɹ
±ɨɫɪɟɞɧɟɧɧɚɹɫɤɨɪɨɫɬɶɞɜɢɠɟɧɢɹɠɢɞɤɨɫɬɢɩɨɫɬɨɹɧɧɚɩɨɜɪɟɦɟɧɢɢɩɨɫɟɱɟɧɢɸ
±ɫɪɟɞɚɧɟɪɟɚɝɟɧɬɨɫɩɨɫɨɛɧɚ
±ɧɟɭɱɢɬɵɜɚɟɬɫɹɨɬɫɤɨɤɱɚɫɬɢɰɨɬɫɬɟɧɨɤɝɢɞɪɨɰɢɤɥɨɧɚ
±ɧɟɭɱɢɬɵɜɚɟɬɫɹɬɟɩɥɨɜɚɹɛɪɨɭɧɨɜɫɤɚɹɤɨɚɝɭɥɹɰɢɹɱɚɫɬɢɰɜɝɢɞɪɨɰɢɤɥɨɧɟ
±ɧɟɭɱɢɬɵɜɚɟɬɫɹɜɥɢɹɧɢɟɬɭɪɛɭɥɟɧɬɧɵɯɩɭɥɶɫɚɰɢɣɫɤɨɪɨɫɬɢɧɚɞɜɢɠɟɧɢɟɱɚɫɬɢɰɵ
Ɉɫɧɨɜɧɚɹɱɚɫɬɶ
Ɋɚɫɫɦɨɬɪɢɦɫɥɭɱɚɣɤɨɝɞɚɞɜɟɤɨɚɝɭɥɢɪɭɸɳɢɟɱɚɫɬɢɰɵɢɦɟɸɬɫɥɟɞɭɸɳɢɟɤɨɨɪɞɢɧɚɬɵɩɟɪ
ɜɚɹɱɚɫɬɢɰɚ²Rș=ɜɬɨɪɚɹ²Rș=ɩɪɢɱɟɦR5 șș==ɪɢɫɚ
Ɋɚɫɫɬɨɹɧɢɟɦɟɠɞɭɞɜɭɦɹɤɨɚɝɭɥɢɪɭɸɳɢɦɢɱɚɫɬɢɰɚɦɢɜɰɢɥɢɧɞɪɢɱɟɫɤɨɣɫɢɫɬɟɦɟɤɨɨɪɞɢ
ɧɚɬɜɵɪɚɡɢɦɢɡɬɟɨɪɟɦɵɤɨɫɢɧɭɫɨɜ
S = s 2 + z 2 ; z = Z 2 − Z1 ;
s 2 = R12 + R22 − 2 ⋅ R1 ⋅ R2 ⋅ cos ( θ1 − θ2 ) .
Ɋɚɡɥɨɠɢɦ))ɧɚɬɚɧɝɟɧɰɢɚɥɶɧɭɸɪɚɞɢɚɥɶɧɭɸɢɚɤɫɢɚɥɶɧɭɸɫɨɫɬɚɜɥɹɸɳɢɟɪɢɫɛɜ
FF′1 = − FF ⋅ cosα1 ;
FFR1 = − FF′1 ⋅ cos ϕ1 ;
FF θ1 = FF′1 ⋅ sin ϕ1 ;
FF′ 2 = − FF ⋅ sin α 2 ;
FFR 2 = − FF′ 2 ⋅ cos ϕ2 ; FF θ 2 = − FF′ 2 ⋅ sin ϕ2 ;
FFZ 1 = FF ⋅ sin α1 ;
FFZ 2 = FF ⋅ cos α 2 .
Выпуск 2
ɊɢɫɄɨɚɝɭɥɹɰɢɹɱɚɫɬɢɰɜɪɚɛɨɱɟɣɤɚɦɟɪɟɦɚɝɧɢɬɧɨɝɨɝɢɞɪɨɰɢɤɥɨɧɚɚ
ɩɪɨɟɤɰɢɢɩɨɨɫɹɦɛɜ
ɁɧɚɱɟɧɢɹFRVijɢFRVijɦɨɝɭɬɛɵɬɶɜɵɪɚɠɟɧɵɢɡɬɟɨɪɟɦɵɤɨɫɢɧɭɫɨɜɡɧɚɱɟɧɢɹFRVĮFRVĮ ±
ɢɡɬɟɨɪɟɦɵɉɢɮɚɝɨɪɚ
129
z
s
; cosα1 = sin α 2 = ;
S
S
R − R1 ⋅ cos(θ1 − θ2 )
R ⋅ sin(θ1 − θ2 ) cos ϕ1 = 2
; sin ϕ1 = 1
;
s
s
R − R2 ⋅ cos(θ1 − θ2 )
R ⋅ sin(θ1 − θ2 )
cos ϕ2 = 1
; sin ϕ2 = 2
.
s
s
sin α1 = cosα 2 =
ɋɢɥɚɤɨɚɝɭɥɹɰɢɢɞɥɹɲɚɪɨɨɛɪɚɡɧɵɯɱɚɫɬɢɰɦɨɠɟɬɛɵɬɶɩɪɟɞɫɬɚɜɥɟɧɚɜɫɥɟɞɭɸɳɟɦɜɢɞɟ>@
π3 ⋅ µ 0 ⋅ d12 ⋅ d 22 ⋅ H1 ⋅ H 2 ⋅ æ1 ⋅ æ 2
FF =
9S 2
ɝɞɟȝ²ɦɚɝɧɢɬɧɚɹɩɨɫɬɨɹɧɧɚɹʌāȽɧɦɇɇ²ɧɚɩɪɹɠɟɧɧɨɫɬɢɦɚɝɧɢɬɧɨɝɨɩɨɥɹɞɥɹɤɚɠ
ɞɨɣɱɚɫɬɢɰɵɫɨɨɬɜɟɬɫɬɜɟɧɧɨȺɦGG²ɞɢɚɦɟɬɪɵɫɮɟɪɢɱɟɫɤɢɯɱɚɫɬɢɰɦ ²ɦɚɝɧɢɬɧɵɟ
ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢɨɟ
Ⱦɥɹɪɚɫɱɟɬɚɦɚɝɧɢɬɧɨɣɫɢɥɵɢɨɩɪɟɞɟɥɟɧɢɹɧɚɩɪɹɠɟɧɧɨɫɬɢɩɨɥɹɜɤɨɧɤɪɟɬɧɨɣɬɨɱɤɟɦɚɝ
ɧɢɬɧɨɝɨɝɢɞɪɨɰɢɤɥɨɧɚɜɨɫɩɨɥɶɡɭɟɦɫɹɪɟɝɪɟɫɫɢɨɧɧɨɣɦɨɞɟɥɶɸɪɚɫɩɪɟɞɟɥɟɧɢɹɩɨɥɹɩɨɪɚɞɢɭɫɭɢ
ɜɵɫɨɬɟ>@
Z ⋅nZ
−

  D  nR
H ( R, Z ) =  H A + ( H 0 − H A ) ⋅ e hC  ⋅  0  
  2 ⋅ R 
ɝɞɟHH$²ɧɚɩɪɹɠɟɧɧɨɫɬɶɩɨɥɹɜɜɟɪɯɧɟɣɢɧɢɠɧɟɣɬɨɱɤɟɪɚɛɨɱɟɣɤɚɦɟɪɟɝɢɞɪɨɰɢɤɥɨɧɚɫɨɨɬ
ɜɟɬɫɬɜɟɧɧɨȺɦh&²ɜɵɫɨɬɚɰɢɥɢɧɞɪɢɱɟɫɤɨɣɱɚɫɬɢɝɢɞɪɨɰɢɤɥɨɧɚɦ'²ɞɢɚɦɟɬɪɜɵɯɨɞɧɨɝɨ
ɩɚɬɪɭɛɤɚɦn= nR²ɩɨɩɪɚɜɨɱɧɵɟɤɨɷɮɮɢɰɢɟɧɬɵɫɥɭɠɚɳɢɟɞɥɹɛɨɥɟɟɬɨɱɧɨɝɨɜɨɫɩɪɨɢɡɜɟɞɟɧɢɹ
ɧɚɩɪɹɠɟɧɧɨɫɬɢɩɨɥɹɜɪɚɛɨɱɟɣɤɚɦɟɪɟɚɩɩɚɪɚɬɚɨɟ
ɉɨɞɫɬɚɜɢɜ ɡɧɚɱɟɧɢɹ ɪɚɞɢɚɥɶɧɨɣ ɬɚɧɝɟɧɰɢɚɥɶɧɨɣ ɢ ɚɤɫɢɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɢɯ ɫɢɥɵ ɤɨɚ
ɝɭɥɹɰɢɢ ± ɜ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ >@ ɩɨɥɭɱɢɦ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɩɪɨɰɟɫɫɚ
ɤɨɚɝɭɥɹɰɢɢɱɚɫɬɢɰɜɝɢɞɪɨɰɢɤɥɨɧɟɫɪɚɞɢɚɥɶɧɵɦɦɚɝɧɢɬɧɵɦɩɨɥɟɦɜɰɢɥɢɧɞɪɢɱɟɫɤɨɣɫɢɫɬɟɦɟ
ɤɨɨɪɞɢɧɚɬ
H ⋅ H ⋅ cos α1 ⋅ cos ϕ1
dR
d 2 R1
 dθ 
;
= R1 ⋅  1  − A1 ⋅ 1 − B1 ⋅ H1 ⋅ dH R1 + E1 ⋅ 1 2
2
dt
dt
S2
 dt 
d 2 θ1
dθ 
H ⋅ H ⋅ cos α1 ⋅ sin ϕ1
2 d θ1 dR1

;
=−
⋅
+ A1 ⋅  U θ − R1 ⋅ 1  − E1 ⋅ 1 2
dt 2
R1 dt dt
S2
dt


d 2 Z1
dZ 
H ⋅ H ⋅ sin α1

;
= g + A1 ⋅  U Z − 1  − B1 ⋅ H1 ⋅ dH Z 1 + E1 ⋅ 1 2 2
2
dt
dt 
R

d 2 R2
dR
H ⋅ H ⋅ sin α 2 ⋅ cos ϕ2  dθ 
;
= R2 ⋅  2  − A2 ⋅ 2 − B2 ⋅ H 2 ⋅ dH R 2 + E2 ⋅ 1 2
2
S2
dt
dt
 dt 
Выпуск 2
H ⋅ H ⋅ sin α 2 ⋅ sin ϕ2
dθ 
d 2 θ2
2 d θ2 dR2

=−
⋅
+ A2 ⋅  U θ − R2 ⋅ 2  + E1 ⋅ 1 2
;
2
S2
dt 
dt
R2 dt dt

130
H ⋅ H ⋅ cos α 2
dZ 
d 2 Z2

;
= g + A2 ⋅  U Z − 2  − B2 ⋅ H 2 ⋅ dH Z 2 + E2 ⋅ 1 2 2
2
S
dt 
dt

2
18µϕWi
µ0 ⋅ æi
; Bi =
;
Ai = 2
di ⋅ CK ⋅ ( ρi − 0, 5ρ f )
( ρi − 0, 5ρ f )
E1 =
2 π2 ⋅ µ 0 ⋅ d 22 ⋅ æ1 ⋅ æ 2
2 π2 ⋅ µ 0 ⋅ d12 ⋅ æ1 ⋅ æ 2
⋅
; E2 = ⋅
;
d1 ⋅ ρ1
d 2 ⋅ ρ2
3
3
nR
Z ⋅n
− i Z   D


hC
0
Hi = H A + ( H0 − H A ) ⋅ e
 ⋅
 .

  2 ⋅ Ri 
Zn
nR
− i Z 

∂H i
n
D 
= −  H A + ( H 0 − H A ) ⋅ e hC  ⋅  0  ⋅ nRR+1 ;
dH Ri =
∂R
  2  Ri

−
∂H i
n
= − Z ⋅ ( H0 − H A ) ⋅ e
dH Zi =
∂Z
hC
Z i nZ
hC
nR
 D 
⋅ 0  ;
 2 ⋅ Ri 
2
S = R12 + R22 − 2 ⋅ R1 ⋅ R2 ⋅ cos ( θ1 − θ2 ) + ( Z 2 − Z1 ) ,
ɝɞɟ—²ɤɨɷɮɮɢɰɢɟɧɬɤɢɧɟɦɚɬɢɱɟɫɤɨɣɜɹɡɤɨɫɬɢɦ ɫij :²ɤɨɷɮɮɢɰɢɟɧɬɧɟɫɮɟɪɢɱɧɨɫɬɢɱɚ
ɫɬɢɰɵ ɨ ɟ &K ² ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɤɰɢɢ Ʉɨɧɧɢɧɝɟɦɚ ɨ ɟ ȡ i ȡ I ² ɩɥɨɬɧɨɫɬɶ ɱɚɫɬɢɰ ɢ
ɜɹɡɤɨɣ ɫɪɟɞɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɤɝɦ L ² ɢɧɞɟɤɫ ɱɚɫɬɢɰɵ 8ș 8 = ² ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɬɚɧɝɟɧ
ɰɢɚɥɶɧɚɹ ɢ ɚɤɫɢɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ ɦɫ J ² ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟ
ɧɢɹ ɦɫ G+Ri G+ =L ² ɱɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɩɨɥɹ >@ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
ɩɨɨɫɹɦRɢ=Ⱥɦ ɋɢɫɬɟɦɚɭɪɚɜɧɟɧɢɣɪɟɲɚɥɚɫɶɱɢɫɥɟɧɧɵɦɦɟɬɨɞɨɦɫɩɨɦɨɳɶɸ0DWK&$'ɞɥɹɱɚɫɬ
ɧɵɯɫɥɭɱɚɟɜɪɢɫɱɚɫɬɢɰɵ²ɠɟɥɟɡɨG G ɦɤɦɫɪɟɞɚ²ɦɚɫɥɨH āȺɦ85 ɦɫ
8ș ɦɫ8= ɦɫ' ɦ' ɦK& ɦ
ɇɚɱɚɥɶɧɵɟɭɫɥɨɜɢɹR ɦ5 ɦș ɪɚɞș ɪɚɞ= ɦ= ɦ
YR YR ɦɫYș Yș ɦɫY= Y= ɦɫ
Ƚɪɚɧɢɱɧɵɦɢɭɫɥɨɜɢɹɦɢɹɜɥɹɟɬɫɹɦɨɦɟɧɬɫɨɭɞɚɪɟɧɢɹɱɚɫɬɢɰɬɟɩɪɨɰɟɫɫɩɪɨɬɟɤɚɟɬɞɨɬɟɯ
ɩɨɪɩɨɤɚɭɞɨɜɥɟɬɜɨɪɹɟɬɫɹɭɫɥɨɜɢɟȡiȡI ɋɥɟɞɭɟɬɨɬɦɟɬɢɬɶɱɬɨɧɚɪɢɫɩɪɢɜɟɞɟɧɵɚɛɫɨɥɸɬɧɵɟɪɚɡɧɨɫɬɢɦɟɠɞɭɤɨɨɪɞɢɧɚɬɚɦɢ
'R R±R'T T±T'= =±=
Выпуск 2
131
ɊɢɫɊɟɡɭɥɶɬɚɬɵɱɢɫɥɟɧɧɨɝɨɢɫɫɥɟɞɨɜɚɧɢɹɦɚɬɟɦɚɬɢɱɟɫɤɨɣɦɨɞɟɥɢ
ɩɪɨɰɟɫɫɚɤɨɚɝɭɥɹɰɢɢɞɜɭɯɱɚɫɬɢɰɜɪɚɛɨɱɟɣɤɚɦɟɪɟɝɢɞɪɨɰɢɤɥɨɧɚɚɛ
ɢɪɚɡɧɢɰɚɦɟɠɞɭɪɚɞɢɚɥɶɧɵɦɢɜɬɚɧɝɟɧɰɢɚɥɶɧɵɦɢɝɢɚɤɫɢɚɥɶɧɵɦɢɞɫɨɫɬɚɜɥɹɸɳɢɦɢ
ȼɵɜɨɞɵ
ɋɨɫɬɚɜɥɟɧɚɦɚɬɟɦɚɬɢɱɟɫɤɚɹɦɨɞɟɥɶɨɩɢɫɵɜɚɸɳɚɹɤɨɚɝɭɥɹɰɢɢɞɜɭɯɱɚɫɬɢɰɜɪɚɛɨɱɟɣɤɚ
ɦɟɪɟɝɢɞɪɨɰɢɤɥɨɧɚɫɪɚɞɢɚɥɶɧɵɦɦɚɝɧɢɬɧɵɦɩɨɥɟɦɜɰɢɥɢɧɞɪɢɱɟɫɤɨɣɫɢɫɬɟɦɟɤɨɨɪɞɢɧɚɬɧɚɨɫ
ɧɨɜɚɧɢɢɩɨɞɯɨɞɚɅɚɝɪɚɧɠɚ
Ⱦɚɧɧɚɹɦɚɬɟɦɚɬɢɱɟɫɤɚɹɦɨɞɟɥɶɛɵɥɚɪɟɲɟɧɚɱɢɫɥɟɧɧɵɦɦɟɬɨɞɨɦɩɪɢɡɚɞɚɧɧɵɯɭɫɥɨ
ɜɢɹɯ
Ɇɚɝɧɢɬɧɨɟɩɨɥɟɫɩɨɫɨɛɫɬɜɭɟɬɩɪɨɰɟɫɫɭɮɥɨɤɭɥɨɨɛɪɚɡɨɜɚɧɢɹɱɬɨɜɫɜɨɸɨɱɟɪɟɞɶɭɜɟɥɢ
ɱɢɜɚɟɬɰɟɧɬɪɨɛɟɠɧɭɸɫɢɥɭɜɝɢɞɪɨɰɢɤɥɨɧɟɜɫɥɟɞɫɬɜɢɟɱɟɝɨɫɬɟɩɟɧɶɨɱɢɫɬɤɢɜɨɡɪɚɫɬɚɟɬ
ɋɩɢɫɨɤɥɢɬɟɪɚɬɭɪɵ
Выпуск 2
ȼɨɡɧɢɰɤɢɣɂȼɋɭɞɨɜɵɟɞɜɢɝɚɬɟɥɢɜɧɭɬɪɟɧɧɟɝɨɫɝɨɪɚɧɢɹɜɬɂȼȼɨɡɧɢɰɤɢɣ²Ɍ ²Ɇ
Ɇɨɪɤɧɢɝɚ²ɫ
Ⱥɥɟɤɫɚɧɞɪɨɜȿȿ>ɢɞɪ@ɉɨɜɵɲɟɧɢɟɪɟɫɭɪɫɚɬɟɯɧɢɱɟɫɤɢɯɫɢɫɬɟɦɩɭɬɟɦɢɫɩɨɥɶɡɨɜɚɧɢɹɷɥɟɤɬɪɢɱɟ
ɫɤɢɯɢɦɚɝɧɢɬɧɵɯɩɨɥɟɣɦɨɧɨɝɪɚɮɢɹȿȿȺɥɟɤɫɚɧɞɪɨɜɂȺɄɪɚɜɟɰȿɇɅɵɫɢɤɨɜ>ɢɞɪ@²ɏɚɪɶɤɨɜ
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