Расчёт И Проектирование Зуборезных Инструментов

РАСЧЕТ И ПРОЕКТИРОВАНИЕ ЗУБОРЕЗНЫХ ИНСТРУМЕНТОВ Прудников Киреев ȼȼȿȾȿɇɂȿ Ʉ ɱɢɫɥɭ ɧɚɢɛɨɥɟɟ ɫɥɨɠɧɵɯ ɢ ɞɨɪɨɝɢɯ ɦɟɬɚɥɥɨɪɟ...

Author: Киреев

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РАСЧЕТ И ПРОЕКТИРОВАНИЕ ЗУБОРЕЗНЫХ ИНСТРУМЕНТОВ Прудников Киреев

ȼȼȿȾȿɇɂȿ Ʉ ɱɢɫɥɭ ɧɚɢɛɨɥɟɟ ɫɥɨɠɧɵɯ ɢ ɞɨɪɨɝɢɯ ɦɟɬɚɥɥɨɪɟɠɭɳɢɯ ɢɧɫɬɪɭɦɟɧɬɨɜ ɨɬɧɨɫɹɬɫɹ ɡɭɛɨɪɟɡɧɵɟ ɢɧɫɬɪɭɦɟɧɬɵ. ȼ ɩɨɫɨɛɢɢ ɩɪɢɜɟɞɟɧɵ ɦɟɬɨɞɵ ɪɚɫɱɟɬɚ ɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɢɧɫɬɪɭɦɟɧɬɨɜ ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɫ ɷɜɨɥɶɜɟɧɬɧɵɦ ɩɪɨɮɢɥɟɦ ɡɭɛɶɟɜ ɜɧɟɲɧɟɝɨ ɡɚɰɟɩɥɟɧɢɹ ɢ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɫ ɷɜɨɥɶɜɟɧɬɧɵɦ ɢ ɩɪɹɦɨɥɢɧɟɣɧɵɦ ɩɪɨɮɢɥɟɦ ɡɭɛɶɟɜ. ɇɚɢɛɨɥɶɲɭɸ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɢ ɬɨɱɧɨɫɬɶ ɨɛɪɚɛɨɬɤɢ ɬɚɤɨɝɨ ɬɢɩɚ ɢɡɞɟɥɢɣ ɨɛɟɫɩɟɱɢɜɚɸɬ ɢɧɫɬɪɭɦɟɧɬɵ, ɪɚɛɨɬɚɸɳɢɟ ɩɨ ɦɟɬɨɞɭ ɰɟɧɬɪɨɢɞɧɨɝɨ ɨɝɢɛɚɧɢɹ - ɨɛɤɚɬɚ. ɂɦɟɧɧɨ ɞɥɹ ɬɚɤɨɝɨ ɬɢɩɚ ɢɧɫɬɪɭɦɟɧɬɨɜ ɪɚɫɫɦɨɬɪɟɧɵ ɫɩɨɫɨɛɵ ɪɚɫɱɟɬɚ ɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ. ȼ ɭɫɥɨɜɢɹɯ ɦɚɫɫɨɜɨɝɨ ɩɪɨɢɡɜɨɞɫɬɜɚ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɢ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ, ɧɚɩɪɢɦɟɪ, ɜ ɚɜɬɨɦɨɛɢɥɟɫɬɪɨɟɧɢɢ, ɢɫɩɨɥɶɡɭɸɬɫɹ ɫɩɟɰɢɚɥɶɧɵɟ ɪɟɠɭɳɢɟ ɢɧɫɬɪɭɦɟɧɬɵ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɡɭɛɨɪɟɡɧɵɣ ɢɧɫɬɪɭɦɟɧɬ ɩɪɨɟɤɬɢɪɭɟɬɫɹ ɞɥɹ ɨɛɤɚɬɤɢ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ ɬɨɥɶɤɨ ɫ ɨɩɪɟɞɟɥɟɧɧɵɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ, ɚ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ ɫ ɨɩɪɟɞɟɥɟɧɧɵɦ ɱɢɫɥɨɦ ɲɥɢɰɟɜ ɢ ɞɪɭɝɢɦɢ ɤɨɧɤɪɟɬɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ. ȼ ɩɨɫɨɛɢɢ ɧɟ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɪɚɫɱɟɬɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɜɨɡɦɨɠɧɨɫɬɶɸ ɩɪɢɦɟɧɟɧɢɹ ɫɬɚɧɞɚɪɬɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɢ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ. Ɉɩɬɢɦɚɥɶɧɨɣ ɤɨɧɫɬɪɭɤɰɢɟɣ ɡɭɛɨɪɟɡɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ ɹɜɥɹɟɬɫɹ ɬɚɤɚɹ ɤɨɧɫɬɪɭɤɰɢɹ, ɤɨɬɨɪɚɹ ɩɪɢ ɩɪɢɦɟɧɟɧɢɢ ɢɧɫɬɪɭɦɟɧɬɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɧɚɢɦɟɧɶɲɢɟ ɡɚɬɪɚɬɵ ɩɨ ɟɝɨ ɷɤɫɩɥɭɚɬɚɰɢɢ ɩɪɢ ɢɡɝɨɬɨɜɥɟɧɢɢ ɨɞɧɨɝɨ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ. ɉɪɢ ɷɬɨɦ ɬɚɤɨɣ ɢɧɫɬɪɭɦɟɧɬ ɞɨɥɠɟɧ ɨɛɟɫɩɟɱɢɜɚɬɶ ɬɪɟɛɭɟɦɨɟ ɤɚɱɟɫɬɜɨ - ɬɨɱɧɨɫɬɶ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɢ ɲɟɪɨɯɨɜɚɬɨɫɬɶ ɩɨɜɟɪɯɧɨɫɬɢ ɡɭɛɶɟɜ. ɉɨɞɯɨɞ ɤ ɨɩɬɢɦɢɡɚɰɢɢ ɤɨɧɫɬɪɭɤɰɢɢ ɡɭɛɨɪɟɡɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ ɬɚɤɠɟ ɪɚɫɫɦɨɬɪɟɧ ɜ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ. Ɋɟɲɟɧɢɟ ɜɨɩɪɨɫɚ ɨɩɬɢɦɢɡɚɰɢɢ ɤɨɧɫɬɪɭɤɰɢɢ, ɤɚɤ ɩɪɚɜɢɥɨ, ɭɫɩɟɲɧɨ ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɨ ɩɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɫ ɩɨɦɨɳɶɸ ɗȼɆ. Ɍɨɱɧɨɫɬɶ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɨɪɟɡɧɵɯ ɢɧɫɬɪɭɦɟɧɬɨɜ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɟɲɟɧɢɟɦ ɬɪɚɧɫɰɟɧɞɟɧɬɧɵɯ ɭɪɚɜɧɟɧɢɣ. Ⱦɚɧ ɚɥɝɨɪɢɬɦ ɪɟɲɟɧɢɹ ɬɚɤɢɯ ɭɪɚɜɧɟɧɢɣ ɧɚ ɗȼɆ. ȼ ɫɜɹɡɢ ɫ ɧɟɞɨɫɬɚɬɨɱɧɨɫɬɶɸ ɢɥɢ ɩɨɥɧɵɦ ɨɬɫɭɬɫɬɜɢɟɦ ɫɬɚɧɞɚɪɬɨɜ ɧɚ ɡɭɛɱɚɬɵɟ ɤɨɥɟɫɚ, ɲɥɢɰɟɜɵɟ ɜɚɥɵ ɢ ɡɭɛɨɪɟɡɧɵɟ ɢɧɫɬɪɭɦɟɧɬɵ ɜ ɛɢɛɥɢɨɬɟɤɟ ɜɭɡɚ, ɜ ɩɨɫɨɛɢɢ ɞɚɧɵ ɧɟɤɨɬɨɪɵɟ ɦɚɬɟɪɢɚɥɵ, ɤɨɬɨɪɵɟ ɨɛɥɟɝɱɚɬ ɩɪɨɰɟɫɫ ɪɚɫɱɟɬɚ ɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɡɭɛɨɪɟɡɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ, ɩɪɢɜɟɞɟɧɵ ɩɪɢɦɟɪɵ ɪɚɫɱɟɬɚ ɢ ɪɚɛɨɱɢɯ ɱɟɪɬɟɠɟɣ ɦɨɧɨɥɢɬɧɨɝɨ ɡɭɛɨɪɟɡɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ. 5

. ɂ ɋ ɏ Ɉ Ⱦ ɇ ɕ ȿ Ⱦ Ⱥ ɇ ɇ ɕ ȿ, ɋ ɉ ɊȺ ȼ Ɉ ɑ ɇ Ⱥ ə ɂ ɇɎ Ɉ Ɋ ɆȺɐɂə Ⱦ Ʌ ə ɉ Ɋ Ɉ ȿ Ʉ Ɍ ɂɊ Ɉ ȼ Ⱥ ɇ ɂ ə Ɂ ɍ ȻɈ Ɋ ȿ Ɂ ɇ ɕ ɏ ɂ ɇ ɋ Ɍ Ɋ ɍ Ɇ ȿ ɇ ɌɈ ȼ ɂ Ɋ Ⱥ ɋ ɑ ȿ Ɍ Ⱦ Ɉ ɉ Ɉ Ʌ ɇ ɂ Ɍ ȿ Ʌ ɖɇ ɕ ɏ Ɍ ȿ ɏ ɇ Ɉ Ʌ Ɉ Ƚ ɂ ɑȿ ɋ Ʉ ɂ ɏ ɉ Ⱥ Ɋ Ⱥ Ɇȿ Ɍ Ɋ Ɉ ȼ Ɂ ɍ Ȼ ɑ Ⱥ Ɍɕ ɏ Ʉ Ɉ Ʌ ȿ ɋ ɂ ɒ Ʌ ɂɐ ȿ ȼ ɕ ɏ ȼȺɅ Ɉ ȼ ȼ ɡɚɞɚɧɢɢ ɧɚ ɤɭɪɫɨɜɨɟ ɢɥɢ ɞɢɩɥɨɦɧɨɟ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɜ ɤɚɱɟɫɬɜɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɩɪɢɜɨɞɹɬɫɹ ɩɚɪɚɦɟɬɪɵ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ ɢ ɫɨɩɪɹɠɟɧɧɨɝɨ ɤɨɥɟɫ ɡɭɛɱɚɬɨɣ ɩɚɪɵ: ɱɢɫɥɨ ɡɭɛɶɟɜ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ z1 ɢ ɫɨɩɪɹɠɟɧɧɨɝɨ z2 ɤɨɥɟɫ; ɦɨɞɭɥɶ m; ɭɝɨɥ ɩɪɨɮɢɥɹ ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɞɢɚɦɟɬɪɟ α; ɤɨɷɮɮɢɰɢɟɧɬ ɜɵɫɨɬɵ ɝɨɥɨɜɤɢ ɡɭɛɚ ha* ; ɝɪɚɧɢɱɧɨɣ ɜɵɫɨɬɵ ɡɭɛɚ hl* ɢ ɧɨɠɤɢ ɡɭɛɚ

h*f ; ɭɝɨɥ ɧɚ-

ɤɥɨɧɚ ɡɭɛɶɟɜ β; ɤɨɷɮɮɢɰɢɟɧɬɵ ɤɨɪɪɟɤɰɢɢ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ x ɢ x2 (ɢɥɢ ɬɨɥɳɢɧɚ ɡɭɛɶɟɜ ɤɨɥɟɫ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ Sn1 ɢ Sn2); ɫɬɟɩɟɧɶ ɬɨɱɧɨɫɬɢ ɩɚɪɵ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɩɨ ɜɫɟɦ ɧɨɪɦɚɦ ɬɨɱɧɨɫɬɢ, ɜɢɞ ɫɨɩɪɹɠɟɧɢɹ ɩɨ ȽɈɋɌ 643-8. Ɇɨɠɟɬ ɛɵɬɶ ɭɤɚɡɚɧɢɟ ɨɛ ɨɛɨɪɭɞɨɜɚɧɢɢ (ɦɨɞɟɥɶ ɫɬɚɧɤɚ), ɧɚ ɤɨɬɨɪɨɦ ɞɨɥɠɧɚ ɜɵɩɨɥɧɹɬɶɫɹ ɨɛɪɚɛɨɬɤɚ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɨɪɟɡɧɵɯ ɢɧɫɬɪɭɦɟɧɬɨɜ ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɹɬɶ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ. Ⱦɢɚɦɟɬɪɵ ɞɟɥɢɬɟɥɶɧɵɯ ɨɤɪɭɠɧɨɫɬɟɣ

d =

mz 2 . mz ; d2 = cos β cos β

(.)

ɍɝɨɥ ɩɪɨɮɢɥɹ ɢ ɦɨɞɭɥɶ ɩɨ ɬɨɪɰɭ (ɬɨɪɰɨɜɵɣ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɢ ɬɨɪɰɨɜɵɣ ɦɨɞɭɥɶ)

d t = arctg

tg α ; m ; mt = cos β cos β

(.2)

ɞɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ α = α ɢ m = m . t t Ⱦɢɚɦɟɬɪɵ ɨɫɧɨɜɧɵɯ ɨɤɪɭɠɧɨɫɬɟɣ

db = d ⋅ cosαt ; d b = d 2 ⋅ cosα t ;

(.3)

2

6

ɍɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɜ ɩɟɪɟɞɚɱɟ ɩɨ ɬɨɪɰɭ ɤɨɥɟɫ α tw ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ, ɢɡɜɟɫɬɧɨ ɢɥɢ ɧɟɢɡɜɟɫɬɧɨ ɦɟɠɨɫɟɜɨɟ ɪɚɫɫɬɨɹɧɢɟ α w . ɉɪɢ ɧɟɡɚɞɚɧɧɨɦ ɦɟɠɨɫɟɜɨɦ ɪɚɫɫɬɨɹɧɢɢ ɞɥɹ ɧɟɤɨɪɪɢɝɢɪɨɜɚɧɧɨɣ ɩɟɪɟɞɚɱɢ, ɤɨɝɞɚ ɯ1 = 0, ɯ2 = 0 ; α tw = α t ɢ Δy = 0 . Ⱦɥɹ ɤɨɪɪɢɝɢɪɨɜɚɧɧɨɣ ɩɟɪɟɞɚɱɢ

(.4)

α tw ɧɚɯɨɞɢɬɫɹ ɩɨɫɥɟ ɨɩɪɟɞɟɥɟɧɢɹ ɢɧɜɨ-

ɥɸɬɵ ɭɝɥɚ

2 ( x + x 2 ) tg α . z + z 2

inv α tw = inv α t +

(.5)

Ɂɧɚɱɟɧɢɟ α ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɪɟɲɟɧɢɹ ɬɪɚɧɫɰɟɧɞɟɧɬɧɨɝɨ ɭɪɚɜɧɟɧɢɹ tw

inv α tw = tg α tw − α tw . Ȼɥɨɤ-ɫɯɟɦɚ ɚɥɝɨɪɢɬɦɚ ɧɚɯɨɠɞɟɧɢɹ ɭɝɥɚ ɩɨ ɡɧɚɱɟɧɢɸ ɟɝɨ ɢɧɜɨɥɸɬɵ ɧɚ ɗȼɆ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ... ɉɪɢɛɥɢɠɟɧɧɨɟ ɡɧɚɱɟɧɢɟ

αtw ɦɨɠɧɨ

ɨɩɪɟɞɟɥɢɬɶ ɩɪɢ ɩɨɦɨɳɢ ɬɚɛɥɢɰ ɢɧɜɨ-

ɥɸɬɧɨɣ ɮɭɧɤɰɢɢ []. Ⱦɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ

inv α w = inv α + ɉɪɢ

α tw = α w 2 ( x + x 2 ) tg α . z + z 2

ɢɡɜɟɫɬɧɨɦ

ɦɟɠɨɫɟɜɨɦ

(.6) ɪɚɫɫɬɨɹɧɢɢ

ɡɭɛɱɚɬɵɯ

α tw = arccos[( d + d 2 ) cos α t 2 a w ] .

ɤɨɥɟɫ (.7)

Ɇɟɠɨɫɟɜɨɟ ɪɚɫɫɬɨɹɧɢɟ

a w = [ 0 ,5 m ( z + z 2 ) cos α t ] (cos α tw ⋅cos β ) .

(.8)

Ʉɨɷɮɮɢɰɢɟɧɬ ɭɪɚɜɧɢɬɟɥɶɧɨɝɨ ɫɦɟɳɟɧɢɹ Δy [2,ɫ.75]:

Δ y = x + x − ⎛⎜ 0 ,5 ( z + z )[( cos α cos α ) − ] cos β ⎞⎟ . t tw 2 ⎠ 2 ⎝ Ⱦɥɹ ɤɨɥɟɫ ɛɟɡ ɫɦɟɳɟɧɢɹ x1 = x 2= 0 ; Δy = 0.

7

(.9)

Ɋɢɫ. .. Ȼɥɨɤ-ɫɯɟɦɚ ɚɥɝɨɪɢɬɦɚ ɧɚɯɨɠɞɟɧɢɹ ɭɝɥɚ ɩɨ ɡɧɚɱɟɧɢɸ ɟɝɨ ɢɧɜɨɥɸɬɵ ɧɚ ɗȼɆ

8

ȼɵɫɨɬɚ ɝɨɥɨɜɤɢ ɡɭɛɶɟɜ ɤɨɥɟɫ

h

a

= ( h * + x − Δ y ) m ; h = ( h* + x − Δ y ) m . a a2 a 2

(.0)

Ⱦɢɚɦɟɬɪɵ ɜɟɪɲɢɧ ɡɭɛɶɟɜ ɤɨɥɟɫ

d

= d + 2(h * + x − Δ y )m ; d = d 2 + 2 ( h * + x − Δ y ) m . (.) a a a2 a 2

ȼɵɫɨɬɚ ɡɭɛɶɟɜ ɤɨɥɟɫ h = (2 h* + C * − Δ y )m , a

(.2)

ɝɞɟ C* - ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɞɢɚɥɶɧɨɝɨ ɡɚɡɨɪɚ (C* = 0,25). ȼɵɫɨɬɚ h ɦɨɠɟɬ ɛɵɬɶ ɩɨɞɫɱɢɬɚɧɚ ɬɚɤɠɟ ɩɨ ɮɨɪɦɭɥɟ: h = (h * + h * )m . a f

(.3)

ȼɵɫɨɬɚ ɧɨɠɤɢ ɡɭɛɶɟɜ ɤɨɥɟɫ hf = h – ha ; hf 2 = h – ha 2 .

(.4)

Ⱦɢɚɦɟɬɪ ɜɩɚɞɢɧ ɡɭɛɶɟɜ ɤɨɥɟɫ df1 = da1 -2h ; df2 = da2 -2h.

(.5)

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɢ ɫɨɩɪɹɠɟɧɧɨɝɨ ɤɨɥɟɫɚ ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɞɢɚɦɟɬɪɟ (ɟɫɥɢ ɧɟ ɭɤɚɡɚɧɚ ɜ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ) Sn1 = 0,5πm + 2 x1⋅m⋅tgα - ECS1; Sn2 = 0,5πm + 2 x2⋅m⋅tgα - ECS2.

(.6)

ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɲɟɜɟɪɨɜ ɪɚɫɱɟɬɧɵɟ ɡɧɚɱɟɧɢɹ Sn1 ɢ Sn2 ɨɩɪɟɞɟɥɹɸɬɫɹ ɫ ɭɱɟɬɨɦ ɩɨɥɨɜɢɧɵ ɜɟɥɢɱɢɧɵ ɞɨɩɭɫɤɚ ɧɚ ɬɨɥɳɢɧɭ ɡɭɛɚ: Sn1 = 0,5πm + 2 x1⋅m⋅tgα - ECS1 -

TC ; 2

Sn2 = 0,5πm + 2 x2⋅m⋅tgα - ECS2 -

TC 2 , 2

ɝɞɟ ECS1 ɢ ECS2 - ɧɚɢɦɟɧɶɲɢɟ ɨɬɤɥɨɧɟɧɢɹ ɬɨɥɳɢɧɵ ɡɭɛɚ ɤɨɥɟɫɚ, ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɪɚɡɨɜɚɧɢɹ ɛɨɤɨɜɨɝɨ ɡɚɡɨɪɚ ɜ ɡɭɛɱɚɬɨɦ ɡɚɰɟɩɥɟɧɢɢ. Ɂɚɜɢɫɹɬ ɨɬ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ ɤɨɥɟɫ ɢ ɜɢɞɚ ɫɨɩɪɹɠɟɧɢɹ. ȼ ɭɱɟɛɧɨɣ ɢ ɧɚɭɱɧɨ-ɬɟɯɧɢɱɟɫɤɨɣ

9

ɥɢɬɟɪɚɬɭɪɟ ɦɨɝɭɬ ɨɛɨɡɧɚɱɚɬɶɫɹ ɫɢɦɜɨɥɚɦɢ ΔS1 ɢ ΔS2. Ⱦɥɹ ɱɚɫɬɢ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɩɨ ȽɈɋɌ 643-8 [3] ɜɟɥɢɱɢɧɵ ECS ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ...

ȼɢɞ ɫɨɩɪɹɠɟɧɢɹ

Ⱦ ɋ ȼ

Ɍɚɛɥɢɰɚ . Ⱦɢɚɦɟɬɪ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ, ɦɦ

ɋɬɟɩɟɧɶ

ɫɜ. 80

ɬɨɱɧɨ- ɞɨ 80 ɫɬɢ 6 7 8 6 7 8 6 7 8

ɞɨ 25

ɫɜ.

ɫɜ.

ɫɜ.

ɫɜ.

ɫɜ.

ɫɜ.

25

80

250

35

400

500

ɞɨ

ɞɨ

ɞɨ

ɞɨ

ɞɨ

ɞɨ

80

250

35

400

500

630

0,06 0,07 0,07 0,09 0, 0,2 0,6 0,8 0,8

0,06 0,07 0,08 0, 0,2 0,4 0,6 0,8 0,2

0,07 0,08 0,09 0, 0,4 0,4 0,8 0,2 0,22

0,08 0,09 0, 0,2 0,4 0,6 0,2 0,22 0,25

0,035 0,04 0,045 0,055 0,035 0,045 0,05 0,06 0,04 0,05 0,06 0,07 0,055 0,06 0,07 0,08 0,06 0,07 0,08 0,09 0,07 0,08 0,09 0, 0,09 0, 0,2 0,4 0, 0,2 0,4 0,4 0, 0,2 0,4 0,6

ɇɚɢɛɨɥɶɲɢɣ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ

ρ a = 0,5 d a2 − d b2 .

(.7)

Ɋɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɜ ɬɨɱɤɟ ɧɚɱɚɥɚ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ

ρ p a = a w ⋅ sin α tw − 0,5 d a22 − d b22 .

(.8)

Ⱦɥɢɧɚ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɥɢɧɢɢ ɡɚɰɟɩɥɟɧɢɹ

L = 0,5( da2 − db2 + da22 − db22 ) − aw ⋅ sinαtw.

(.9)

ɇɟɨɛɯɨɞɢɦɨɟ ɩɪɢ ɲɟɜɢɧɝɨɜɚɧɢɢ ɩɟɪɟɤɪɵɬɢɟ ɨɛɪɚɛɨɬɤɨɣ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ

ΔL = 0,5m sin α tw .

(.20)

ɍɝɨɥ ɧɚɤɥɨɧɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɧɚ ɨɫɧɨɜɧɨɦ ɰɢɥɢɧɞɪɟ ɤɨɥɟɫɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɬɨɪɰɭ (ɞɥɹ ɤɨɫɨɡɭɛɵɯ ɤɨɥɟɫ) 0

σ = arccos(cos α ⋅ sin β) .

(.2)

Ⱦɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ σ = 90° . Ʉɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɤɪɵɬɢɹ ɨɛɪɚɛɨɬɤɨɣ ɩɪɢ ɡɚɰɟɩɥɟɧɢɢ ɤɨɥɟɫɚ ɫ ɲɟɜɟɪɨɦ

ε = ( L + ΔL) πm ⋅ (sin σ ⋅ cosα )

(.22)

Ⱦɨɥɠɧɨ ɛɵɬɶ ε ≥ ,. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɲɟɜɢɧɝɨɜɚɧɢɟ ɧɟɜɨɡɦɨɠɧɨ. ɢ ɲɟɜɟɪ ɧɟ ɩɪɨɟɤɬɢɪɭɟɬɫɹ. ȼ ɡɚɞɚɧɢɢ ɧɚ ɤɭɪɫɨɜɨɟ ɢɥɢ ɞɢɩɥɨɦɧɨɟ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɜ ɤɚɱɟɫɬɜɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɦɨɝɭɬ ɛɵɬɶ ɭɤɚɡɚɧɵ ɧɨɦɟɪɚ ɱɟɪɬɟɠɟɣ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ, ɦɟɠɰɟɧɬɪɨɜɨɟ ɪɚɫɫɬɨɹɧɢɟ ɩɨ ɫɛɨɪɨɱɧɨɦɭ ɱɟɪɬɟɠɭ ɭɡɥɚ ɢɥɢ ɞɟɬɚɥɶɧɨɦɭ ɤɨɪɩɭɫɚ ɭɡɥɚ, ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɢɡɝɨɬɨɜɥɟɧɢɹ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ. ȼ ɱɟɪɬɟɠɚɯ ɦɨɠɟɬ ɜɫɬɪɟɬɢɬɶɫɹ ɞɸɣɦɨɜɚɹ ɫɢɫɬɟɦɚ ɦɟɪ. Ɋɚɡɥɢɱɚɸɬ ɞɢɚɦɟɬɪɚɥɶɧɵɣ ɢ ɨɤɪɭɠɧɨɣ ɩɢɬɱ. Ⱦɢɚɦɟɬɪɚɥɶɧɵɣ ɩɢɬɱ ɜɵɪɚɠɚɟɬ ɱɢɫɥɨ ɡɭɛɶɟɜ, ɩɪɢɯɨɞɹɳɢɯɫɹ ɧɚ ɞɸɣɦ ɞɢɚɦɟɬɪɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ. ɉɢɬɱ ɢ ɦɨɞɭɥɶ ɫɜɹɡɚɧɵ ɡɚɜɢɫɢɦɨɫɬɶɸ m = 25,4 / p, ɦɦ,

(.23)

ɝɞɟ p - ɞɢɚɦɟɬɪɚɥɶɧɵɣ ɩɢɬɱ. Ɉɤɪɭɠɧɨɣ ɩɢɬɱ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɲɚɝ ɦɟɠɞɭ ɡɭɛɶɹɦɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ, ɜɵɪɚɠɟɧɧɵɣ ɜ ɞɸɣɦɚɯ. Ɇɟɠɞɭ ɨɤɪɭɠɧɵɦ ɩɢɬɱɟɦ P, ɞɢɚɦɟɬɪɚɥɶɧɵɦ ɩɢɬɱɟɦ p ɢ ɦɨɞɭɥɟɦ m ɫɭɳɟɫɬɜɭɟɬ ɡɚɜɢɫɢɦɨɫɬɶ: P = π/p , ɞɸɣɦ; P = π⋅ m/25,4, ɞɸɣɦ; m = 8,09P, ɦɦ.

(.24)

ɏɨɪɞɚɥɶɧɵɣ ɩɢɬɱ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɲɚɝ ɦɟɠɞɭ ɡɭɛɶɹɦɢ ɩɨ ɯɨɪɞɟ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ, ɜɵɪɚɠɟɧɧɨɣ ɜ ɞɸɣɦɚɯ. ȼ ɱɟɪɬɟɠɚɯ ɦɨɠɟɬ ɜɫɬɪɟɬɢɬɶɫɹ ɢ ɞɜɭɯɦɨɞɭɥɶɧɚɹ (ɢɥɢ ɞɜɭɯɩɢɬɱɟɜɚɹ) ɫɢɫɬɟɦɚ ɡɚɰɟɩɥɟɧɢɹ, ɧɚɩɪɢɦɟɪ m1/m2. ȼ ɷɬɨɣ ɫɢɫɬɟɦɟ ɪɚɡɦɟɪɵ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɢ ɬɨɥɳɢɧɵ ɡɭɛɶɟɜ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɩɨ ɛɨɥɶɲɨɦɭ ɦɨɞɭɥɸ, ɚ ɜɵɫɨɬɵ ɡɭɛɶɟɜ - ɩɨ ɦɚɥɨɦɭ ɦɨɞɭɥɸ, ɬ.ɟ. ɤɨɥɟɫɚ ɢɦɟɸɬ ɭɤɨɪɨɱɟɧɧɭɸ ɩɪɨɬɢɜ ɨɛɵɱɧɨɣ ɜɵɫɨɬɭ ɡɭɛɶɟɜ. ɇɚ ɱɟɪɬɟɠɟ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ ɦɨɠɟɬ ɛɵɬɶ ɭɤɚɡɚɧɚ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɡɭɛɚ ɬɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɯɨɪɞɟ Sx ɢ ɜɵɫɨɬɚ ɝɨɥɨɜɤɢ ɡɭɛɚ ɞɨ ɯɨɪ

ɞɵ ɢ ɧɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ. Ɍɨɝɞɚ ɜɵɫɨɬɚ ɝɨɥɨɜɤɢ ɡɭɛɚ

ha ɢ

ɬɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɞɭɝɟ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ Sn1 ɩɨɞɫɱɢɬɵɜɚɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ: ⎛ ⎞⎤ S d ⎡⎢ ⎜ x ⎟⎟⎥⎥ ; h =h − ⎢−cos⎜⎜ arcsin a x 2 ⎢ d cos β ⎟⎟⎥⎥ ⎜ ⎝ ⎠⎦ ⎣⎢

Sn = d⋅cos β ⋅ arcsin ( Sx /(d⋅ cos β).

(.25)

ɇɚ ɱɟɪɬɟɠɟ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ ɦɨɠɟɬ ɛɵɬɶ ɭɤɚɡɚɧ ɪɚɡɦɟɪ Ʉ ɩɨ ɪɨɥɢɤɚɦ (ɲɚɪɢɤɚɦ) ɞɢɚɦɟɬɪɚ dɒ. Ɍɨɝɞɚ ɞɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ ɫ ɱɟɬɧɵɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ ɬɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɞɭɝɟ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɦɨɠɟɬ ɛɵɬɶ ɩɨɞɫɱɢɬɚɧɚ ɩɨ ɮɨɪɦɭɥɚɦ: M=

⎛ d cosα ⎞ K − dɒ ⎟; ; α D = arccos⎜ 2 ⎝ 2M ⎠

Sn = d(

dɒ π + inv αD – inv α ). d cosα z

(.26)

Ⱦɥɹ ɧɟɱɟɬɧɨɝɨ ɱɢɫɥɚ ɡɭɛɶɟɜ ɤɨɥɟɫɚ ɪɚɡɦɟɪ

K − dɒ M= π ; 2 cos 2z

(.27)

ɚ ɜɟɥɢɱɢɧɵ αD ɢ Sn ɩɨɞɫɱɢɬɵɜɚɸɬɫɹ ɬɚɤ ɠɟ, ɩɨ ɮɨɪɦɭɥɚɦ (.26). Ⱦɥɹ ɤɨɫɨɡɭɛɵɯ ɤɨɥɟɫ ɪɚɡɦɟɪ Ɇ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɞɥɹ ɩɪɹɦɨɡɭɛɵɯ, ɬ.ɟ. ɩɨ ɮɨɪɦɭɥɚɦ: M=

K − dɒ - ɞɥɹ ɱɟɬɧɨɝɨ ɱɢɫɥɚ ɡɭɛɶɟɜ ɤɨɥɟɫɚ ɢ 2

K − dɒ M= π - ɞɥɹ ɧɟɱɟɬɧɨɝɨ ɱɢɫɥɚ ɡɭɛɶɟɜ. 2 cos 2z Ɂɞɟɫɶ ɜɟɥɢɱɢɧɚ Ʉ - ɨɯɜɚɬɵɜɚɸɳɢɣ ɪɚɡɦɟɪ ɩɨ ɲɚɪɢɤɚɦ. Ɍɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɧɨɪɦɚɥɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɫɨɡɭɛɨɝɨ ɤɨɥɟɫɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ: 2

⎛ tgα ⎞ ⎟ d cos⎜⎜ arctg cos β ⎟⎠ ⎝ αD = ; 2M ó = arccos[cos (arctg

tg á )sin â] ; cos â

⎤ ⎡ ⎥ ⎢ ⎛ dɒ tgα ⎞⎥ ⎢ ⎟ . − invα D + inv⎜⎜ arctg Sn1= π ⋅ m – d1cos β ⎢ cos β ⎟⎠⎥ ⎛ tgα ⎞ ⎝ ⎟⎟ sin σ ⎥ ⎢ d ⋅ cos⎜⎜ arctg β cos ⎝ ⎠ ⎣⎢ ⎦⎥

(.28)

Ɋɚɫɱɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɫ ɷɜɨɥɶɜɟɧɬɧɵɦɢ ɡɭɛɶɹɦɢ ɧɟ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɪɚɫɱɟɬɚ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ. Ɉɫɨɛɟɧɧɨɫɬɶɸ ɪɚɫɱɟɬɚ ɡɭɛɨɪɟɡɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ (ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ, ɞɨɥɛɹɤɨɜ) ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɹɜɥɹɟɬɫɹ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ ɞɢɚɦɟɬɪɚ ɨɤɪɭɠɧɨɫɬɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɧɚɱɚɥɭ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɜɚɥɚ dp . ȿɫɥɢ ɷɬɨɬ ɞɢɚɦɟɬɪ ɧɚ ɱɟɪɬɟɠɟ ɧɟ ɭɤɚɡɚɧ, ɬɨ ɫɥɟɞɭɟɬ ɨɛɪɚɬɢɬɶɫɹ ɤ ɫɬɚɧɞɚɪɬɭ ɧɚ ɲɥɢɰɟɜɵɟ ɫɨɟɞɢɧɟɧɢɹ ɋɌ ɋɗȼ 268-76 [4]. Ⱥ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɜ ɬɨɱɤɟ ɧɚɱɚɥɚ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɜɚɥɚ ɪɚɫɫɱɢɬɚɬɶ ɩɨ ɮɨɪɦɭɥɟ: 2

2

⎛d ⎞ ⎛d ⎞ ρP = ⎜ P ⎟ − ⎜ b ⎟ . ⎝ 2 ⎠ ⎝ 2 ⎠

(.29)

ɋ ɰɟɥɶɸ ɭɜɟɥɢɱɟɧɢɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɢ ɬɨɱɧɨɫɬɢ ɢɡɝɨɬɨɜɥɟɧɢɹ ɲɥɢɰɟɜɵɟ ɜɚɥɵ ɫ ɩɪɹɦɨɥɢɧɟɣɧɵɦ ɩɪɨɮɢɥɟɦ ɡɭɛɶɟɜ ɩɨ ȽɈɋɌ 39-80 ɢɥɢ ɫɩɟɰɢɚɥɶɧɵɟ ɨɛɪɚɛɚɬɵɜɚɸɬɫɹ ɬɚɤɠɟ ɩɨ ɦɟɬɨɞɭ ɨɛɤɚɬɚ ɫ ɩɨɦɨɳɶɸ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɢ ɞɨɥɛɹɤɨɜ. ɇɚ ɪɢɫ..2 ɩɪɟɞɫɬɚɜɥɟɧɵ ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ ɢ ɜɚɪɢɚɧɬɵ ɟɝɨ ɢɫɩɨɥɧɟɧɢɹ ɩɨ ȽɈɋɌ 39-80 [5]. ɇɚ ɪɢɫ..2 ɨɛɨɡɧɚɱɟɧɢɹ: D - ɧɨɦɢɧɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɧɚɪɭɠɧɨɝɨ ɞɢɚɦɟɬɪɚ; d(d)- ɧɨɦɢɧɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɜɧɭɬɪɟɧɧɟɝɨ ɞɢɚɦɟɬɪɚ; b - ɧɨɦɢɧɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɲɢɪɢɧɵ ɡɭɛɚ. 3

Ɋɢɫ..2. ȼɚɪɢɚɧɬɵ ɢɫɩɨɥɧɟɧɢɹ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɩɨ ȽɈɋɌ 39-80 Ⱥ,ɋ – ɰɟɧɬɪɢɪɨɜɚɧɢɟ ɩɨ ɜɧɭɬɪɟɧɧɟɦɭ ɞɢɚɦɟɬɪɭ d; ȼ – ɰɟɧɬɪɢɪɨɜɚɧɢɟ ɩɨ ɧɚɪɭɠɧɨɦɭ ɞɢɚɦɟɬɪɭ D.

4

Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɨɛɨɡɧɚɱɟɧɢɟ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ ɜɯɨɞɢɬ ɱɢɫɥɨ ɲɥɢɰɟɜ z. ɂɫɩɨɥɧɟɧɢɟ ɜɚɥɨɜ Ⱥ ɢ ɋ ɩɪɟɞɧɚɡɧɚɱɚɟɬɫɹ ɞɥɹ ɲɥɢɰɟɜɨɝɨ ɫɨɟɞɢɧɟɧɢɹ ɫ ɰɟɧɬɪɢɪɨɜɚɧɢɟɦ ɩɨ ɜɧɭɬɪɟɧɧɟɦɭ ɞɢɚɦɟɬɪɭ d. ɑɟɪɜɹɱɧɵɟ ɮɪɟɡɵ ɞɥɹ ɜɚɥɨɜ ɢɫɩɨɥɧɟɧɢɹ Ⱥ ɫɨɟɞɢɧɟɧɢɣ ɬɹɠɟɥɨɣ ɫɟɪɢɢ ɧɟ ɩɪɟɞɭɫɦɨɬɪɢɜɚɸɬ [5]. ȼɚɥɵ ɢɫɩɨɥɧɟɧɢɹ ȼ ɩɪɟɞɧɚɡɧɚɱɚɸɬɫɹ ɞɥɹ ɲɥɢɰɟɜɨɝɨ ɫɨɟɞɢɧɟɧɢɹ ɫ ɰɟɧɬɪɢɪɨɜɚɧɢɟɦ ɩɨ ɧɚɪɭɠɧɨɦɭ ɞɢɚɦɟɬɪɭ D . Ⱦɢɚɦɟɬɪ d1, ɜ ɢɫɩɨɥɧɟɧɢɢ Ⱥ ɨɩɪɟɞɟɥɹɟɬ ɝɥɭɛɢɧɭ ɤɚɧɚɜɨɤ, ɜ ɢɫɩɨɥɧɟɧɢɢ ȼ - ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɞɨ ɜɧɭɬɪɟɧɧɟɣ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ. ȽɈɋɌɨɦ 39-80 ɪɟɝɥɚɦɟɧɬɢɪɭɸɬɫɹ ɡɧɚɱɟɧɢɹ ɜɟɥɢɱɢɧɵ ɮɚɫɤɢ ɋ ɢ ɪɚɞɢɭɫɚ r ɜ ɨɫɧɨɜɚɧɢɢ ɲɥɢɰɚ ɜɚɥɚ ɢɫɩɨɥɧɟɧɢɹ ɋ, ɪɚɡɦɟɪɚ aɐ ɜɚɥɚ ɢɫɩɨɥɧɟɧɢɹ Ⱥ. ɉɪɢɦɟɪ ɭɫɥɨɜɧɨɝɨ ɨɛɨɡɧɚɱɟɧɢɹ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ ɫ ɱɢɫɥɨɦ ɡɭɛɶɟɜ (ɲɥɢɰɟɜ) z = 8, ɜɧɭɬɪɟɧɧɢɦ ɞɢɚɦɟɬɪɨɦ d = 36 ɦɦ, ɧɚɪɭɠɧɵɦ ɞɢɚɦɟɬɪɨɦ D = 40 ɦɦ, ɫ ɰɟɧɬɪɢɪɨɜɚɧɢɟɦ ɩɨ ɜɧɭɬɪɟɧɧɟɦɭ ɞɢɚɦɟɬɪɭ: d - 8 ɯ 36ɟ8 ɯ 40ɚ11 ɯ 7f8. Ɍɨ ɠɟ ɫ ɰɟɧɬɪɢɪɨɜɚɧɢɟɦ ɩɨ ɧɚɪɭɠɧɨɦɭ ɞɢɚɦɟɬɪɭ: D - 8 x 36 x 40f7 x 7h8. Ʉɪɨɦɟ ɪɚɡɦɟɪɨɜ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɜɚɥɚ ɫ ɞɨɩɭɫɤɨɦ ɞɨɥɠɧɵ ɛɵɬɶ ɢɡɜɟɫɬɧɵ ɫɥɟɞɭɸɳɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɞɚɧɧɵɟ: ɦɚɬɟɪɢɚɥ, ɢɡ ɤɨɬɨɪɨɝɨ ɢɡɝɨɬɚɜɥɢɜɚɟɬɫɹ ɲɥɢɰɟɜɵɣ ɜɚɥ; ɟɝɨ ɬɟɪɦɨɨɛɪɚɛɨɬɤɚ; ɞɢɚɦɟɬɪ ɭɫɬɭɩɚ ɢɥɢ ɛɭɪɬɢɤɚ ɜ ɤɨɧɰɟ ɲɥɢɰɟɜɨɝɨ ɩɪɨɮɢɥɹ; ɫɬɚɧɨɤ, ɧɚ ɤɨɬɨɪɨɦ ɛɭɞɟɬ ɨɛɪɚɛɚɬɵɜɚɬɶɫɹ ɡɚɝɨɬɨɜɤɚ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ. ȿɫɥɢ ɜ ɡɚɞɚɧɢɢ ɧɚ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɢɧɫɬɪɭɦɟɧɬɚ ɧɟɬ ɞɚɧɧɵɯ ɨ ɞɢɚɦɟɬɪɟ ɭɫɬɭɩɚ (ɛɭɪɬɢɤɚ), ɬɨ Dɭɫɬ ɫɥɟɞɭɟɬ ɩɪɢɧɹɬɶ ɪɚɜɧɵɦ D. Ⱦɚɧɧɵɟ ɩɨ ɫɬɚɧɤɭ ɢɦɟɸɬɫɹ ɜ [6]. Ɍɚɦ ɠɟ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɫɜɟɞɟɧɢɹ, ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɬɟɯɧɢɤɨ-ɷɤɨɧɨɦɢɱɟɫɤɨɝɨ ɨɛɨɫɧɨɜɚɧɢɹ ɫɩɪɨɟɤɬɢɪɨɜɚɧɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ. Ɋɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɨɟɤɬɢɪɨɜɚɬɶ ɱɟɪɜɹɱɧɵɟ ɮɪɟɡɵ ɞɥɹ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɫ ɩɪɚɜɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɢ ɥɟɜɵɦɢ ɫɬɪɭɠɟɱɧɵɦɢ ɤɚɧɚɜɤɚɦɢ. Ⱦɥɹ ɨɛɪɚɛɨɬɤɢ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɢɫɩɨɥɧɟɧɢɹ Ⱥ (ɪɢɫ..2) ɩɪɨɟɤɬɢɪɭɟɬɫɹ ɱɟɪɜɹɱɧɚɹ ɮɪɟɡɚ ɫ ɭɫɢɤɚɦɢ (ɪɢɫ..3, ɚ), ɞɥɹ ɜɚɥɨɜ ɢɫɩɨɥɧɟɧɢɹ ȼ ɢ ɋ - ɱɟɪɜɹɱɧɵɟ ɮɪɟɡɵ ɛɟɡ ɭɫɢɤɨɜ (ɪɢɫ..3, ɛ). 5

ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɞɥɹ ɜɚɥɢɤɚ ɢɫɩɨɥɧɟɧɢɹ ɋ, ɧɟɨɛɯɨɞɢɦɨ ɜɵɞɟɪɠɚɬɶ ɭɫɥɨɜɢɟ: dɩɤ. ≤ (d + 2Cmax),

(.30)

ɝɞɟ dɩɤ - ɞɢɚɦɟɬɪ ɨɤɪɭɠɧɨɫɬɢ, ɫ ɤɨɬɨɪɨɣ ɧɚɱɢɧɚɟɬɫɹ ɩɟɪɟɯɨɞɧɚɹ ɤɪɢɜɚɹ ɜ ɨɫɧɨɜɚɧɢɢ ɲɥɢɰɚ ɡɭɛɚ; Cmax - ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɮɚɫɤɢ ɧɚ ɧɚɪɭɠɧɨɦ ɞɢɚɦɟɬɪɟ ɲɥɢɰɟɜɨɣ ɜɬɭɥɤɢ. ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɞɥɹ ɜɚɥɢɤɚ ɢɫɩɨɥɧɟɧɢɹ ȼ, ɧɟɨɛɯɨɞɢɦɨ ɜɵɞɟɪɠɚɬɶ ɭɫɥɨɜɢɟ: dɩɤ. ≤ d .

(.3)

ɉɪɢ ɧɟɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɣ .30 ɢ .3 ɧɟɜɨɡɦɨɠɧɨ ɫɨɟɞɢɧɟɧɢɟ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ ɢ ɲɥɢɰɟɜɨɣ ɜɬɭɥɤɢ. ȿɫɥɢ ɬɨɱɧɨɫɬɶ ɪɚɡɦɟɪɨɜ d ɢ b ɧɟ ɩɪɟɜɵɲɚɟɬ 8 ɤɜɚɥɢɬɟɬɚ (ɬ.ɟ. 8, 9, 0 ɢ ɬ.ɞ.) ɢ ɧɟ ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹ ɡɚɤɚɥɤɚ ɜɚɥɨɜ ɩɨɫɥɟ ɲɥɢɰɟɮɪɟɡɟɪɨɜɚɧɢɹ, ɬɨ ɪɚɫɱɟɬɧɵɟ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɜɚɥɚ ɩɨɞɫɱɢɬɵɜɚɸɬɫɹ ɩɨ ɧɢɠɟɫɥɟɞɭɸɳɢɦ ɮɨɪɦɭɥɚɦ. Ɋɚɫɱɟɬɧɵɣ ɧɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ Dp (ɢɫɩɨɥɧɟɧɢɟ Ⱥ, ȼ, ɋ): Dp = Dmax - 2Cmin ,

(.32)

ɝɞɟ Dmax - ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɧɚɪɭɠɧɨɝɨ ɞɢɚɦɟɬɪɚ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ; Cmin - ɦɢɧɢɦɚɥɶɧɵɣ ɪɚɡɦɟɪ ɮɚɫɤɢ ɧɚ ɜɟɪɲɢɧɟ ɲɥɢɰɚ ɡɭɛɚ. Ɋɚɫɱɟɬɧɵɣ ɜɧɭɬɪɟɧɧɢɣ ɞɢɚɦɟɬɪ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ dɊ ɜɚɥɨɜ ɢɫɩɨɥɧɟɧɢɹ Ⱥ ɢ ɋ: dɊ = dmin + 0,25T,

(.33)

ɝɞɟ dmin - ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɜɧɭɬɪɟɧɧɟɝɨ ɞɢɚɦɟɬɪɚ d ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ; Ɍ - ɞɨɩɭɫɤ ɧɚ ɜɧɭɬɪɟɧɧɢɣ ɞɢɚɦɟɬɪ. Ⱦɥɹ ɜɚɥɚ ɢɫɩɨɥɧɟɧɢɹ ȼ dP = d1.

(.34)

Ɋɚɫɱɟɬɧɚɹ ɲɢɪɢɧɚ ɲɥɢɰɚ ɡɭɛɚ (ɢɫɩɨɥɧɟɧɢɟ Ⱥ, ȼ, ɋ) bɊ = bmin + 0,25T1,

(.35)

6

Ɋɢɫ. .3. ɑɟɪɜɹɱɧɨ-ɲɥɢɰɟɜɚɹ ɮɪɟɡɚ: ɚ) ɫ ɭɫɢɤɚɦɢ; ɛ) ɛɟɡ ɭɫɢɤɨɜ.

ɝɞɟ bmin - ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɲɢɪɢɧɵ ɡɭɛɚ ɜɚɥɚ; T1 - ɞɨɩɭɫɤ ɧɚ ɲɢɪɢɧɭ ɡɭɛɚ. ȿɫɥɢ ɬɨɱɧɨɫɬɶ ɪɚɡɦɟɪɨɜ d ɢ b ɩɪɟɜɵɲɚɟɬ 8 ɤɜɚɥɢɬɟɬ (7, 6 ɢ ɬ.ɞ.) ɢɥɢ ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹ ɡɚɤɚɥɤɚ ɜɚɥɨɜ ɩɨɫɥɟ ɲɥɢɰɟɮɪɟɡɟɪɨɜɚɧɢɹ, ɬɨ ɪɚɫɱɟɬɧɵɟ

7

ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɞɨɥɠɧɵ ɭɱɢɬɵɜɚɬɶ ɩɪɢɩɭɫɤ ɧɚ ɩɨɫɥɟɞɭɸɳɟɟ ɲɥɢɮɨɜɚɧɢɟ ɩɨɜɟɪɯɧɨɫɬɟɣ. Ɂɧɚɱɟɧɢɟ ɩɪɢɩɭɫɤɚ ɭɤɚɡɵɜɚɟɬɫɹ ɜ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ ɢɡɝɨɬɨɜɥɟɧɢɹ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ. ȿɫɥɢ ɬɚɤɢɯ ɞɚɧɧɵɯ ɧɟɬ, ɬɨ ɢɯ ɫɥɟɞɭɟɬ ɨɩɪɟɞɟɥɢɬɶ. ɋɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɩɪɢɩɭɫɤɚ ɧɚ ɜɧɭɬɪɟɧɧɢɣ ɞɢɚɦɟɬɪ d ɢ ɲɢɪɢɧɭ ɡɭɛɚ b ɦɨɠɧɨ ɩɨɞɫɱɢɬɚɬɶ ɩɨ ɮɨɪɦɭɥɟ: Ɋɫɪ = 0,0042 d + 0,12 .

(.36)

Ɍɨɝɞɚ ɪɚɫɱɟɬɧɵɟ ɡɧɚɱɟɧɢɹ dɪ ɢ bɪ ɞɥɹ ɜɚɥɨɜ ɢɫɩɨɥɧɟɧɢɹ Ⱥ ɢ ɋ ɛɭɞɭɬ ɪɚɜɧɵ: dɪ = dmin + Pɫɪ;

bɪ = bmin + Pɫɪ .

(.37)

Ⱦɥɹ ɜɚɥɚ ɢɫɩɨɥɧɟɧɢɹ ȼ: dɪ = d1;

bɪ = bmin + Pɫɪ .

(.38)

Ɋɚɫɱɟɬɧɨɟ ɡɧɚɱɟɧɢɟ ɧɚɪɭɠɧɨɝɨ ɞɢɚɦɟɬɪɚ Dp ɩɨɞɫɱɢɬɵɜɚɟɬɫɹ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɞɥɹ ɱɢɫɬɨɜɵɯ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ.

8

ɊȺɋɑȿɌ ɂ ɉɊɈȿɄɌɂɊɈȼȺɇɂȿ ɑȿɊȼəɑɇɕɏ ɁɍȻɈɊȿɁɇɕɏ ɎɊȿɁ ɇɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɮɪɟɡɵ dɚɨ, ɞɢɚɦɟɬɪ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ dɨɬɜ, ɞɥɢɧɚ ɮɪɟɡɵ L ɢ ɫɩɨɫɨɛ ɤɪɟɩɥɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɩɪɨɞɢɤɬɨɜɚɧɵ ɤɨɧɤɪɟɬɧɵɦɢ ɭɫɥɨɜɢɹɦɢ ɩɪɢɦɟɧɟɧɢɹ ɧɚ ɫɬɚɧɤɟ ɧɚɫɚɞɧɵɯ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ [7]. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɫɩɟɰɢɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɩɚɪɚɦɟɬɪɵ dɚɨ, dɨɬɜ, L ɰɟɥɶɧɵɯ ɱɟɪɜɹɱɧɨ-ɦɨɞɭɥɶɧɵɯ ɮɪɟɡ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɜɵɛɢɪɚɬɶ ɢɡ ɬɚɛɥ.2. ɫ ɭɱɟɬɨɦ ɡɚɦɟɱɚɧɢɣ ɤ ɧɟɣ.

Ɍɚɛɥɢɰɚ 2.

Ɇɨɞɭɥɶ m, ɦɦ

– ,25 ,25-,375 ,375-,75 ,5-2 2-2,25 2,25-2,75 2,5-2,75 3-3,5 3-3,75 3,75-4,5 4-4,5 5 5-5,5 5,5-6 6-7 6,5-7 8-0 8 9 0 2 4

Ɏɪɟɡɵ ɩɨɞ ɲɟɜɟɪ ɢ ɨɛɳɟɝɨ ɧɚɡɧɚɱɟɧɢɹ Ⱦɥɢɧɚ ɮɪɟɡɵ, Ⱦɢɚɦɟɬɪ, ɦɦ ɦɦ ɇɚɪɭɠɧɵɣ dɚɨ 40 50 63 7 80 90

ɄɨɪɨɬȾɥɢɧɈɬɜɟɪɫɬɢɹ ɤɨɣ ɧɨɣ dɨɬɜ 6 22 27 27 32 32

32 40 50 56 7 80

40

2

60

32 50 70 80 200 224

9

7

80

32

80

90

40

90

00

40

00

2

40

2

25

50

25

40

50

40

60

60

55

80

60

80

40

2

40 40 50 50 50 50

32

25

40

25 40 50 60 70 90

7

00

00

8

Ⱦɥɢɧɚ, ɇɚɪɭɠɈɬɜɟɪL, ɦɦ ɧɵɣ ɫɬɢɹ dɚɨ dɨɬɜ

90

32

40

Ⱦɢɚɦɟɬɪ, ɦɦ

50 70

00

8

ɉɪɟɰɢɡɢɨɧɧɵɟ ɮɪɟɡɵ

60 80 80 200 -

ɉɪɢɦɟɱɚɧɢɹ: . Ɋɚɡɦɟɪɵ ɨɬɧɨɫɹɬɫɹ ɤ ɦɨɧɨɥɢɬɧɵɦ ɢɥɢ ɫɨɫɬɚɜɧɵɦ (ɫ ɩɪɢɜɚɪɟɧɧɵɦɢ ɪɟɣɤɚɦɢ) ɮɪɟɡɚɦ. 2. Ʉ ɩɪɟɰɢɡɢɨɧɧɵɦ ɨɬɧɨɫɹɬɫɹ ɮɪɟɡɵ ɤɥɚɫɫɚ ɬɨɱɧɨɫɬɢ ȺȺ; ɤ ɮɪɟɡɚɦ ɨɛɳɟɝɨ ɧɚɡɧɚɱɟɧɢɹ, ɢɫɩɨɥɶɡɭɟɦɵɦ ɧɚ ɱɢɫɬɨɜɨɣ ɢ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɨɛɪɚɛɨɬɤɟ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ, - ɮɪɟɡɵ ɤɥɚɫɫɨɜ Ⱥ,ȼ,ɋ Ⱦ ɫ Ɍɍ ɩɨ ȽɈɋɌ 9324-80. 3. Ɋɟɤɨɦɟɧɞɭɟɦɵɟ ɧɚɡɧɚɱɟɧɢɹ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ: ɤɥɚɫɫɚ ȺȺ - ɞɥɹ ɤɨɥɟɫ 7-ɣ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ; ɤɥɚɫɫɚ Ⱥ - 8-ɣ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ; ɤɥɚɫɫɚ ȼ - 9-ɣ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ; ɤɥɚɫɫɚ ɋ,Ⱦ - 0-ɣ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ. 4. ɑɟɪɜɹɱɧɵɟ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ ɞɨɥɠɧɵ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɤɥɚɫɫɭ ȼ; ɪɟɠɟ ɤɥɚɫɫɭ Ⱥ. 5. Ƚɚɛɚɪɢɬɧɵɟ ɪɚɡɦɟɪɵ ɦɧɨɝɨɡɚɯɨɞɧɵɯ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɜɵɛɢɪɚɬɶ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɞɥɹ ɩɪɟɰɢɡɢɨɧɧɵɯ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɨɡɦɨɠɧɨ ɭɜɟɥɢɱɟɧɢɟ ɞɥɢɧɵ ɮɪɟɡɵ. Ɍɚɤ ɤɚɤ ɜ ɧɚɲɟɣ ɫɬɪɚɧɟ ɭ ɛɨɥɶɲɢɧɫɬɜɚ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɲɥɢɮɭɸɬɫɹ ɡɚɞɧɢɟ ɩɨɜɟɪɯɧɨɫɬɢ ɡɭɛɶɟɜ, ɬɨ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɬɨɥɶɤɨ ɫɨ ɲɥɢɮɨɜɚɧɧɵɦ ɩɪɨɮɢɥɟɦ ɡɭɛɶɟɜ, ɬ.ɟ. ɫ ɞɜɨɣɧɵɦ ɡɚɬɵɥɨɜɚɧɢɟɦ. ɑɢɫɥɨ ɡɚɯɨɞɨɜ ɱɢɫɬɨɜɵɯ ɮɪɟɡ i = . ɑɢɫɥɨ ɡɚɯɨɞɨɜ ɮɪɟɡ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ ; ɜ ɦɚɫɫɨɜɨɦ ɩɪɨɢɡɜɨɞɫɬɜɟ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɫ ɧɟɱɟɬɧɵɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ ɢɧɨɝɞɚ ɩɪɢɧɢɦɚɟɬɫɹ i = 2, ɫ ɱɟɬɧɵɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ - i = 3. ɋɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɭɜɟɥɢɱɟɧɢɟ ɱɢɫɥɚ ɡɚɯɨɞɨɜ ɮɪɟɡɵ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɩɨɝɪɟɲɧɨɫɬɟɣ ɲɚɝɚ ɡɭɛɶɟɜ ɢɡ-ɡɚ ɩɨɝɪɟɲɧɨɫɬɟɣ ɞɟɥɟɧɢɹ ɧɚ ɡɚɯɨɞɵ ɩɪɢ ɢɡɝɨɬɨɜɥɟɧɢɢ ɢɧɫɬɪɭɦɟɧɬɚ. ɑɢɫɥɨ ɡɭɛɶɟɜ z0 (ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ) ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɜɵɛɢɪɚɟɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɥɚɫɫɚ ɬɨɱɧɨɫɬɢ ɢ ɦɨɞɭɥɹ. Ⱦɥɹ ɩɪɟɰɢɡɢɨɧɧɵɯ (ɤɥɚɫɫɚ ȺȺ) ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɢ ɮɪɟɡ ɦɧɨɝɨɡɚɯɨɞɧɵɯ (i>) ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɦɨɞɭɥɹ m ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɧɢɦɚɬɶ: m = - ,75 ɦɦ -

z0 = 6;

m = 2 - 5,5 ɦɦ -

z0 = 4; 20

m = 6 - 0 ɦɦ

- z0 = 2.

Ⱦɥɹ ɱɢɫɬɨɜɵɯ ɢ ɱɟɪɧɨɜɵɯ ɮɪɟɡ ɨɛɳɟɝɨ ɧɚɡɧɚɱɟɧɢɹ, ɨɞɧɨɡɚɯɨɞɧɵɯ ɮɪɟɡ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ, ɬ.ɟ. ɫ ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɵɦ ɩɪɨɮɢɥɟɦ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɧɢɦɚɬɶ: m = - 2,75 ɦɦ - z0 = 2; m = 3 - 6 ɦɦ

-

z0 = 0;

m = 6,5 - 2 ɦɦ - z0 = 9. Ƚɟɨɦɟɬɪɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ ɮɪɟɡɵ: ɩɟɪɟɞɧɢɣ ɭɝɨɥ γɜ=0°, ɡɚɞɧɢɣ ɭɝɨɥ α ɜ = 9 ÷2°. ɍɜɟɥɢɱɟɧɢɟ ɩɟɪɟɞɧɟɝɨ ɢ ɡɚɞɧɟɝɨ ɭɝɥɚ ɞɨ ɨɩɪɟɞɟɥɟɧɧɵɯ ɩɪɟɞɟɥɨɜ ɭɜɟɥɢɱɢɜɚɟɬ ɩɟɪɢɨɞ ɫɬɨɣɤɨɫɬɢ ɢɧɫɬɪɭɦɟɧɬɚ. ɍɜɟɥɢɱɟɧɢɟ ɩɟɪɟɞɧɟɝɨ ɭɝɥɚ γɜ ɞɨ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɞɥɹ ɤɚɠɞɨɝɨ ɦɨɞɭɥɹ ɡɧɚɱɟɧɢɹ ɩɨɡɜɨɥɹɟɬ ɭɜɟɥɢɱɢɬɶ ɬɨɱɧɨɫɬɶ ɩɪɨɮɢɥɹ ɧɚɪɟɡɚɟɦɨɝɨ ɷɬɢɦ ɢɧɫɬɪɭɦɟɧɬɨɦ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ [7], ɧɨ ɭɜɟɥɢɱɢɜɚɟɬ ɬɪɭɞɧɨɫɬɢ ɩɟɪɟɬɨɱɤɢ ɢɧɫɬɪɭɦɟɧɬɚ. ɇɚ ɩɪɨɢɡɜɨɞɫɬɜɟ ɩɨ ɩɭɬɢ ɭɜɟɥɢɱɟɧɢɹ ɩɟɪɟɞɧɟɝɨ ɭɝɥɚ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟ ɢɞɭɬ. ɂɡ-ɡɚ ɬɪɭɞɧɨɫɬɟɣ ɲɥɢɮɨɜɚɧɢɹ ɡɚɞɧɢɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɡɭɛɶɟɜ ɮɪɟɡ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɡɚɞɧɟɝɨ ɭɝɥɚ ɟɝɨ ɧɟ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɭɜɟɥɢɱɢɜɚɬɶ ɛɨɥɶɲɟ 2°. ɉɚɞɟɧɢɟ ɡɚɬɵɥɤɚ ɨɫɧɨɜɧɨɝɨ ɡɚɬɵɥɨɜɚɧɢɹ Ʉ=

πd z

ao tg α . ɜ 0

(2.)

Ɂɧɚɱɟɧɢɟ Ʉ ɨɤɪɭɝɥɹɟɬɫɹ ɞɨ 0,5 ɦɦ ɢɥɢ ɰɟɥɨɝɨ ɱɢɫɥɚ. ɉɚɞɟɧɢɟ ɡɚɬɵɥɤɚ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɡɚɬɵɥɨɜɚɧɢɹ (ɨɫɭɳɟɫɬɜɥɹɟɦɨɝɨ ɩɪɢ ɩɨɦɨɳɢ ɪɟɡɰɚ ɞɨ ɬɟɪɦɢɱɟɫɤɨɣ ɨɛɪɚɛɨɬɤɢ) Ʉ = (,5 - 2)Ʉ.

(2.2)

Ɂɧɚɱɟɧɢɟ Ʉ ɬɚɤɠɟ ɨɤɪɭɝɥɹɟɬɫɹ ɞɨ 0,5 ɦɦ ɢɥɢ ɰɟɥɨɝɨ ɱɢɫɥɚ. Ⱦɚɥɶɧɟɣɲɢɣ ɪɚɫɱɟɬ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɢɧɫɬɪɭɦɟɧɬɚ ɡɚɜɢɫɢɬ ɨɬ ɨɫɨɛɟɧɧɨɫɬɟɣ ɩɪɨɮɢɥɢɪɨɜɚɧɢɹ ɡɭɛɶɟɜ ɮɪɟɡɵ, ɫɜɹɡɚɧɧɵɯ ɫ ɭɫɥɨɜɢɹɦɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɧɫɬɪɭɦɟɧɬɚ.

2

2.1. Ɋɚɫɱɟɬ ɪɚɡɦɟɪɨɜ ɩɪɨɮɢɥɹ ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɩɪɟɰɢɡɢɨɧɧɵɯ, ɱɢɫɬɨɜɵɯ ɢ ɮɪɟɡ ɨɛɳɟɝɨ ɧɚɡɧɚɱɟɧɢɹ ɛɟɡ ɦɨɞɢɮɢɤɚɰɢɢ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ȿɫɥɢ ɨɬɫɭɬɫɬɜɭɸɬ ɬɪɟɛɨɜɚɧɢɹ ɩɨ ɪɚɛɨɬɟ ɩɟɪɟɯɨɞɧɵɯ ɤɪɢɜɵɯ ɧɚ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫɚɯ, ɞɨɩɭɫɤɚɟɬɫɹ ɩɨɞɪɟɡ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ, ɬɨ ɪɚɫɱɟɬ ɪɚɡɦɟɪɨɜ ɩɪɨɮɢɥɹ ɡɭɛɱɚɬɨɣ ɪɟɣɤɢ ɩɪɨɢɡɜɨɞɢɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ɍɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɤ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɟ ɫɟɱɟɧɢɢ

α w0 = α .

(2.3)

ȼɵɫɨɬɚ ɝɨɥɨɜɤɢ ɡɭɛɚ

ha 0 = hf .

(2.4)

ȼɵɫɨɬɚ ɧɨɠɤɢ ɡɭɛɚ

hf 0 = ha + C ⋅ m,

(2.5)

ɝɞɟ ɋ - ɤɨɷɮɮɢɰɢɟɧɬ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɡɚɡɨɪ ɦɟɠɞɭ ɜɩɚɞɢɧɨɣ ɡɭɛɶɟɜ ɪɟɣɤɢ ɢ ɜɟɪɲɢɧɨɣ ɡɭɛɶɟɜ ɤɨɥɟɫɚ; ɋ = 0,25 - ɩɪɢ m ≤ 3 ɦɦ ɢ ɋ = 0,3 – ɩɪɢ m > 3 ɦɦ. ȼɵɫɨɬɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ h0 = ha 0 + hf 0 .

(2.6)

Ɋɚɞɢɭɫ ɫɤɪɭɝɥɟɧɢɹ ɛɨɤɨɜɨɣ ɢ ɜɟɪɲɢɧɧɨɣ ɤɪɨɦɨɤ ɡɭɛɚ ɮɪɟɡɵ rɝ = 0,2 m

ɢɥɢ rɝ = 0,1m / (1 - sin αw0 ).

(2.7)

Ɂɧɚɱɟɧɢɟ rɝ ɨɤɪɭɝɥɹɟɬɫɹ ɞɨ ɞɟɫɹɬɵɯ ɞɨɥɟɣ ɦɦ. Ɋɚɞɢɭɫ ɫɤɪɭɝɥɟɧɢɹ ɛɨɤɨɜɨɣ ɪɟɠɭɳɟɣ ɤɪɨɦɤɢ ɢ ɜɩɚɞɢɧɵ rH = 0,3 m.

(2.8)

Ɂɧɚɱɟɧɢɟ rH ɨɤɪɭɝɥɹɟɬɫɹ ɞɨ ɞɟɫɹɬɵɯ ɞɨɥɟɣ ɦɦ. ɒɚɝ ɡɭɛɶɟɜ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɩɪɹɦɨɣ ɡɭɛɶɟɜ ɪɟɣɤɢ Ɋt 0 = πm.

(2.9)

Ɍɨɥɳɢɧɚ ɡɭɛɶɟɜ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɩɪɹɦɨɣ ɡɭɛɶɟɜ ɪɟɣɤɢ

22

St 0 = πm- Sn .

(2.0)

ȼɵɫɨɬɚ ɡɭɛɚ (ɝɥɭɛɢɧɚ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ) ɮɪɟɡɵ Hk = h0 +

k + k + (1,5 ÷3) - ɞɥɹ ɮɪɟɡ ɫ m < 4 ɦɦ 2

ɢ Hk = h0 +

k + k + (1,5 ÷3) + hɤɚɧ - ɞɥɹ ɮɪɟɡ ɫ m ≥ 4 ɦɦ. 2

(2.) (2.2)

Ʉɚɧɚɜɤɚ ɩɨ ɞɧɭ ɜɩɚɞɢɧɵ ɦɟɠɞɭ ɡɭɛɶɹɦɢ ɪɟɣɤɢ ɢɡɝɨɬɚɜɥɢɜɚɟɬɫɹ ɞɥɹ ɨɛɥɟɝɱɟɧɢɹ ɲɥɢɮɨɜɚɧɢɹ ɛɨɤɨɜɵɯ ɫɬɨɪɨɧ ɡɭɛɶɟɜ hɤɚɧ = - 2 ɦɦ; rɤɚɧ = 0,5 - ɦɦ; bɤɚɧ = Sn - 2hf0⋅ tgαw 0 - 1.

(2.3)

ȿɫɥɢ bɤɚɧ ≤ ɦɦ, ɬɨ ɤɚɧɚɜɤɚ ɧɟ ɞɟɥɚɟɬɫɹ. Ɂɧɚɱɟɧɢɟ ɇɤ ɨɤɪɭɝɥɹɟɬɫɹ ɫ ɤɪɚɬɧɨɫɬɶɸ ɚ0 = 0,5 ɜ ɛɨɥɶɲɭɸ ɫɬɨɪɨɧɭ. ɍɝɨɥ ɩɪɨɮɢɥɹ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ θ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ 22° ɢɥɢ 25° ɢɥɢ 30°. Ȼóɥɶɲɟɟ ɡɧɚɱɟɧɢɟ ɨɛɥɟɝɱɚɟɬ ɩɪɨɰɟɫɫ ɡɚɬɵɥɨɜɚɧɢɹ ɮɪɟɡ ɪɟɡɰɨɦ, ɭɜɟɥɢɱɢɜɚɟɬ ɨɛɴɟɦ ɩɪɨɫɬɪɚɧɫɬɜɚ ɞɥɹ ɪɚɡɦɟɳɟɧɢɹ ɫɬɪɭɠɤɢ. Ɋɚɞɢɭɫ ɡɚɤɪɭɝɥɟɧɢɹ ɜ ɨɫɧɨɜɚɧɢɢ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ r = π(dɚ 0 -2ɇɤ ) / 10z0,

(2.4)

ɢ ɪɟɡɭɥɶɬɚɬ ɨɤɪɭɝɥɹɟɬɫɹ ɫ ɤɪɚɬɧɨɫɬɶɸ ɚ0 = 0,5. Ɇɟɬɨɞɨɦ ɝɪɚɮɢɱɟɫɤɨɝɨ ɩɨɫɬɪɨɟɧɢɹ ɨɩɪɟɞɟɥɢɬɶ ɞɨɫɬɚɬɨɱɧɨɫɬɶ ɞɥɢɧɵ ɩɪɨɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɡɚɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɡɭɛɶɟɜ ɮɪɟɡɵ (ɪɢɫ.2.). Ɇɟɬɨɞ ɩɨɫɬɪɨɟɧɢɹ, ɩɪɢɜɟɞɟɧɧɵɣ ɧɚ ɪɢɫ. 2., ɧɟ ɬɪɟɛɭɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɩɨɹɫɧɟɧɢɣ. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɫɱɢɬɚɬɶ ɢ ɩɪɢɧɹɬɶ ɡɧɚɱɟɧɢɟ ɞɢɚɦɟɬɪɚ ɲɥɢɮɨɜɚɥɶɧɨɝɨ ɤɪɭɝɚ Dɒ: Dɒ = 25 + 2ɇɤ + 5.

(2.5)

ɇɨ Dɒ ɞɨɥɠɟɧ ɛɵɬɶ ɧɟ ɦɟɧɶɲɟ 60 ɦɦ. ɍɝɥɨɜɨɣ ɲɚɝ ε = 360°/ z0 .

(2.6)

ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɫɬɪɨɟɧɢɹ ɨɩɪɟɞɟɥɹɸɬɫɹ ɭɝɥɵ:

εɒ - ɰɟɧɬɪɚɥɶɧɵɣ ɭɝɨɥ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɩɪɚɜɢɥɶɧɨ ɩɪɨɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɡɭɛɚ ɮɪɟɡɵ; 23

ε ′- ɰɟɧɬɪɚɥɶɧɵɣ ɭɝɨɥ, ɤɨɬɨɪɵɣ ɫ ɧɟɡɧɚɱɢɬɟɥɶɧɵɦɢ ɞɨɩɭɳɟɧɢɹɦɢ ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɡɚ ɭɝɨɥ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɞɥɢɧɟ ɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɡɭɛɚ ɮɪɟɡɵ. Ⱦɭɝɚ ȺȾ ɨɩɪɟɞɟɥɹɟɬ ɞɥɢɧɭ ɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ, ɚ ɞɭɝɚ Ⱥɋ - ɜɫɸ ɞɥɢɧɭ ɡɚɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɡɭɛɚ ɮɪɟɡɵ.

Ɋɢɫ. 2.. Ƚɪɚɮɢɱɟɫɤɨɟ ɩɨɫɬɪɨɟɧɢɟ ɤ ɨɩɪɟɞɟɥɟɧɢɸ ɞɨɫɬɚɬɨɱɧɨɫɬɢ ɞɥɢɧɵ ɩɪɨɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɡɚɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɡɭɛɚ ɮɪɟɡɵ.

ɍɫɥɨɜɢɟɦ ɞɨɫɬɚɬɨɱɧɨɫɬɢ ɞɥɢɧɵ ɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɡɭɛɚ ɮɪɟɡɵ ɹɜɥɹɟɬɫɹ: - ɞɥɹ m ≤ 4 ɦɦ - ∪ȺȾ ≥ 0,5∪Ⱥɋ; ɞɥɹ m > 4 ɦɦ - ∪ȺȾ ≥ 0,3∪Ⱥɋ

(2.7)

ȿɫɥɢ ɭɫɥɨɜɢɟ (2.7) ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɫɥɟɞɭɟɬ ɭɜɟɥɢɱɢɬɶ ɭɝɨɥ θ, ɥɢɛɨ ɭɦɟɧɶɲɢɬɶ ɡɧɚɱɟɧɢɟ Ʉ (ɭɦɟɧɶɲɢɬɶ ɡɚɞɧɢɣ ɭɝɨɥ), ɥɢɛɨ ɭɦɟɧɶɲɢɬɶ ɱɢɫɥɨ ɡɭɛɶɟɜ (ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ) ɮɪɟɡɵ z0 . ɉɪɢɱɟɦ αɜ ɦɨɠɟɬ ɛɵɬɶ ɭɦɟɧɶɲɟɧ ɞɨ 24

ɬɚɤɨɝɨ ɡɧɚɱɟɧɢɹ, ɤɨɬɨɪɨɟ ɩɨɡɜɨɥɢɥɨ ɛɵ ɧɚ ɛɨɤɨɜɵɯ ɪɟɠɭɳɢɯ ɤɪɨɦɤɚɯ ɢɦɟɬɶ ɡɚɞɧɢɣ ɭɝɨɥ αɛ ≥ (,5÷2)°, ɬ.ɟ. arctg (tgαɜ ⋅ sinαw0 ) ≥ (,5÷2)°.

(2.8)

ɋ ɩɨɦɨɳɶɸ ɗȼɆ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɞɨɫɬɚɬɨɱɧɨɫɬɶ ɩɪɨɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɡɭɛɶɟɜ ɮɪɟɡɵ ɧɚ ɨɫɧɨɜɟ ɚɧɚɥɢɬɢɱɟɫɤɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ [8]. ɋɪɟɞɧɢɣ ɪɚɫɱɟɬɧɵɣ ɞɢɚɦɟɬɪ ɮɪɟɡɵ Dt =da0 - 2ha 0 - (0,4÷0,5)k.

(2.9)

Ɂɧɚɱɟɧɢɟ Dt ɨɤɪɭɝɥɹɟɬɫɹ ɫ ɤɪɚɬɧɨɫɬɶɸ 0,0 ɦɦ. ɍɝɨɥ ɧɚɤɥɨɧɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɰɢɥɢɧɞɪɟ

ω t = arcsin(m⋅ i /Dt ).

(2.20)

Ɂɧɚɱɟɧɢɟ ωt ɩɨɞɫɱɢɬɵɜɚɟɬɫɹ ɫ ɬɨɱɧɨɫɬɶɸ ″ . ɇɚɩɪɚɜɥɟɧɢɟ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɩɪɚɜɨɟ, ɟɫɥɢ ɩɪɨɟɤɬɢɪɭɟɬɫɹ ɮɪɟɡɚ ɞɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ ɢɥɢ ɤɨɫɨɡɭɛɵɯ ɤɨɥɟɫ ɫ ɩɪɚɜɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɡɭɛɶɟɜ. Ⱦɥɹ ɤɨɫɨɡɭɛɵɯ ɤɨɥɟɫ ɫ ɥɟɜɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɡɭɛɶɟɜ ɩɪɨɟɤɬɢɪɭɟɬɫɹ ɮɪɟɡɚ ɫ ɥɟɜɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɡɭɛɶɟɜ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɩɪɢɦɟɧɹɸɬɫɹ ɱɟɪɜɹɱɧɵɟ ɮɪɟɡɵ ɫɨ ɫɬɪɭɠɟɱɧɵɦɢ ɤɚɧɚɜɤɚɦɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɦɢ ɩɨɞ ɩɪɹɦɵɦ ɭɝɥɨɦ ɤ ɜɢɧɬɨɜɨɣ ɧɚɪɟɡɤɟ, wk= wt, ɫ ɜɢɧɬɨɜɵɦɢ ɫɬɪɭɠɟɱɧɵɦɢ ɤɚɧɚɜɤɚɦɢ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦ ɧɚɩɪɚɜɥɟɧɢɸ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɦɨɠɧɨ ɩɪɨɟɤɬɢɪɨɜɚɬɶ ɱɟɪɜɹɱɧɵɟ ɮɪɟɡɵ ɫ wt ≤ 3° ɫ ɩɪɹɦɵɦɢ ɫɬɪɭɠɟɱɧɵɦɢ ɤɚɧɚɜɤɚɦɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɦɢ ɜɞɨɥɶ ɨɫɢ ɮɪɟɡɵ, ɬ.ɟ. wk = 0°. ɒɚɝ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ

Ρz =

π ⋅ Dt tgω ; ɞɥɹ ωk= 0° − Pz = ∞. k

(2.2)

ɒɚɝ ɜɢɬɤɨɜ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɩɨ ɨɫɢ ɮɪɟɡɵ

Ρx 0 =

Ρt 0 ⋅ i . cos ωt

(2.22)

25

ɍɝɨɥ ɭɫɬɚɧɨɜɤɢ ɮɪɟɡɵ ɧɚ ɫɬɚɧɤɟ

ψ = β ± ωt .

(2.23)

Ɂɧɚɤ «+» ɛɟɪɟɬɫɹ ɩɪɢ ɪɚɡɧɨɢɦɟɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɜɢɬɤɨɜ ɮɪɟɡɵ ɢ ɡɭɛɶɟɜ ɤɨɥɟɫɚ, ɡɧɚɤ « - » - ɩɪɢ ɨɞɧɨɢɦɟɧɧɨɦ. ɉɪɨɮɢɥɢɪɨɜɚɧɢɟ ɮɪɟɡɵ ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɨ ɧɚ ɨɫɧɨɜɟ ɚɪɯɢɦɟɞɨɜɚ ɢ ɤɨɧɜɨɥɸɬɧɨɝɨ ɱɟɪɜɹɤɚ. ɑɢɫɬɨɜɵɟ ɱɟɪɜɹɱɧɵɟ ɮɪɟɡɵ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɨɮɢɥɢɪɨɜɚɬɶ ɧɚ ɨɫɧɨɜɟ ɚɪɯɢɦɟɞɨɜɚ ɱɟɪɜɹɤɚ, ɱɟɪɧɨɜɵɟ - ɧɚ ɨɫɧɨɜɟ ɤɨɧɜɨɥɸɬɧɨɝɨ ɱɟɪɜɹɤɚ. Ɋɚɛɨɱɢɣ ɱɟɪɬɟɠ ɱɢɫɬɨɜɨɣ ɮɪɟɡɵ ɞɨɥɠɟɧ ɫɨɞɟɪɠɚɬɶ ɩɪɨɮɢɥɶ ɡɭɛɶɟɜ ɮɪɟɡɵ ɫ ɪɚɡɦɟɪɚɦɢ ɜ ɧɨɪɦɚɥɶɧɨɦ ɢ ɨɫɟɜɨɦ ɫɟɱɟɧɢɢ ɩɥɨɫɤɨɫɬɶɸ ɤ ɜɢɬɤɚɦ ɮɪɟɡɵ, ɱɟɪɧɨɜɨɣ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ (ɩɨɞ ɞɚɥɶɧɟɣɲɭɸ ɱɢɫɬɨɜɭɸ ɨɛɪɚɛɨɬɤɭ ɢɥɢ ɞɥɹ ɧɢɡɤɢɯ ɫɬɟɩɟɧɟɣ ɬɨɱɧɨɫɬɢ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ) - ɬɨɥɶɤɨ ɩɪɨɮɢɥɶ ɡɭɛɶɟɜ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ.

ɍɝɨɥ ɩɪɨɮɢɥɹ ɜ ɨɫɟɜɨɦ ɫɟɱɟɧɢɢ ɨɫɧɨɜɧɨɝɨ ɚɪɯɢɦɟɞɨɜɚ ɱɟɪɜɹɤɚ

α Ɉɋ = arctg

tgα w0 , cos ω t

(2.24)

ɝɞɟ αw 0 - ɭɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ. ɍɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɨɫɟɜɨɦ ɫɟɱɟɧɢɢ ɫ ɩɪɚɜɨɣ αxR0 ɢ ɫ ɥɟɜɨɣ

αxL0 ɫɬɨɪɨɧɵ (ɜɢɞ ɧɚ ɩɟɪɟɞɧɸɸ ɩɨɜɟɪɯɧɨɫɬɶ ɡɭɛɚ ɮɪɟɡɵ) ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ: α xR0 = arctg

Pz ⋅ tgα Ɉɋ ; Pz # ɤ ⋅ z 0 ⋅ tgα Ɉɋ

α xL 0 = arctg

Pz ⋅ tgα Ɉɋ . Pz ± ɤ ⋅ z 0 ⋅ tgα Ɉɋ

(2.25)

ȼ ɮɨɪɦɭɥɚɯ ɜɟɪɯɧɢɟ ɡɧɚɤɢ ( «-», «+» ) ɨɬɧɨɫɹɬɫɹ ɤ ɩɪɚɜɨɡɚɯɨɞɧɵɦ ɮɪɟɡɚɦ, ɧɢɠɧɢɟ («+», «-»)- ɤ ɥɟɜɨɡɚɯɨɞɧɵɦ. ɉɪɢ wk= 0°, αxR0=αxL0= =αɈɋ . Ɉɫɟɜɨɣ ɲɚɝ ɡɭɛɶɟɜ ɮɪɟɡɵ

PɈɋ .O =

Pto . cos ωt

(2.26)

Ɍɨɥɳɢɧɚ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɨɫɟɜɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɞɢɚɦɟɬɪɟ

S Ɉɋ .O =

St o . cos ωt

(2.27)

26

Ⱦɢɚɦɟɬɪ d1 ɢ ɞɥɢɧɭ ɛɭɪɬɢɤɨɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ l ɩɪɢɧɢɦɚɬɶ ɢɡ ɬɚɛɥ. 2.2 (ɩɪɟɰɢɡɢɨɧɧɵɟ ɮɪɟɡɵ) ɢ ɢɡ ɬɚɛɥ. 2.3 (ɮɪɟɡɵ ɨɛɳɟɝɨ ɧɚɡɧɚɱɟɧɢɹ ɢ ɩɨɞ ɲɟɜɟɪ). Ɍɚɛɥɢɰɚ 2.2 dao, ɦɦ 7 80 90 00 2 25 40 60 80 200 225

d1, ɦɦ 50 55 60 65 70 80 85 90 95 00 20

l, ɦɦ 5 ~“~ ~“~ ~“~ ~“~ ~“~ ~“~ ~“~ ~“~ ~“~ ~“~ Ɍɚɛɥɢɰɚ 2.3

dao, ɦɦ 40 50 63-7 80-00 2-40 60-80

d1, ɦɦ 26 33 40 50 60 75

l, ɦɦ 4 ~“~ ~“~ ~“~ 5 5

ɉɪɟɠɞɟ ɱɟɦ ɨɩɪɟɞɟɥɢɬɶ ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɭɸ ɞɥɢɧɭ ɪɚɛɨɱɟɣ ɱɚɫɬɢ LP , ɢɫɯɨɞɹ ɢɡ ɞɥɢɧɵ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɥɢɧɢɢ ɡɚɰɟɩɥɟɧɢɹ ɮɪɟɡɵ ɢ ɤɨɥɟɫɚ, ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɫɱɢɬɚɬɶ: - ɭɝɨɥ ɞɚɜɥɟɧɢɹ (ɩɪɨɮɢɥɹ) ɧɚ ɝɨɥɨɜɤɟ ɡɭɛɚ ɤɨɥɟɫɚ d

α a = arccos

d

b

;

a

- ɭɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɮɪɟɡɵ ɢ ɤɨɥɟɫɚ ɜ ɬɨɪɰɨɜɨɦ ɫɟɱɟɧɢɢ ɤɨɥɟɫɚ

α wt 0 = arctg

tgα

w0 . cos β

27

Ɇɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɚɹ ɞɥɢɧɚ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɮɪɟɡɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:

L

⎡ = ⎢⎛⎜ d a ⋅sin α a − d ⋅sin α ω p ⎣⎝ t0

⎤ ⎞⋅cos α cos ⋅ ψ ⎟ ωt 0 ⎥⎦ cos β + 2 POC .O ⎠

(2.28)

ɉɪɨɜɟɪɢɬɶ ɞɨɫɬɚɬɨɱɧɨɫɬɶ ɞɥɢɧɵ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɬɚɛɥ. 2.. ȿɫɥɢ L≥(lp+ +2l), ɬɨ ɩɪɢɧɢɦɚɟɬɫɹ ɬɚɛɥɢɱɧɨɟ ɡɧɚɱɟɧɢɟ L. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ L = lp+2l. Ɋɚɡɦɟɪɵ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ ɢ ɞɨɩɭɫɤɢ ɧɚ ɪɚɡɦɟɪɵ ɧɚɡɧɚɱɚɸɬɫɹ ɩɨ ɬɚɛɥ. 2.4. Ɍɚɛɥɢɰɚ 2.4. ɇɨɦɢɧɚɥɶɧɵɣ ɞɢɚɦɟɬɪ ɨɬɜɟɪɫɬɢɹ ɮɪɟɡɵ, dɨɬɜ, ɦɦ 6

Ɋɚɡɦɟɪ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ ȼɵɫɨɬɚ ɩɚɡɚ ɨɬ ɒɢɪɢɧɚ ɩɚɡɚ bn, ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɣ Ɋɚɞɢɭɫ ɡɚɫɬɨɪɨɧɵ ɨɬɜɟɪɦɦ ɤɪɭɝɥɟɧɢɹ ɜ ɫɬɢɹ ɋ, ɦɦ ɩɚɡɭ R, ɦɦ ɇɨɦɢ- Ⱦɨɩɭɫɤ ɇɨɦɢ- Ⱦɨɩɭɫɤ ɧɚɥ ɧɚɥ 4 ɋ 7,7 ɇ2 0,4+0,2

Ⱦɨɩɭɫɤɚɟɦɨɟ ɫɦɟɳɟɧɢɟ ɩɚɡɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɨɬɜ. 0,07

22

6

ɋ

24

ɇ2

0,7+0,3

0,09

27

7

ɋ

29,8

ɇ2

0,9+0,3

0,09

32

8

ɋ

34,8

ɇ2

0,9+0,3

0,09

40

0

ɋ

43,5

ɇ2

0,9+0,3

0,09

50

2

ɋ

53,5

ɇ2

+0,5

0,2

60

4

ɋ

64,2

ɇ2

,+0,5

0,2

ɉɨ ɬɪɟɛɨɜɚɧɢɸ ɡɚɤɚɡɱɢɤɚ ɭ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɤɨɫɨɡɭɛɵɯ ɤɨɥɟɫ β >20° ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹ ɡɚɛɨɪɧɵɣ ɤɨɧɭɫ ɫ ɩɚɪɚɦɟɬɪɚɦɢ: ɞɥɢɧɚ ɤɨɧɭɫɚ lɄ = 6 m; ɭɝɨɥ ɤɨɧɭɫɚ ϕɄ = 8° .

(2.29)

Ⱦɥɢɧɚ ɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɨɬɜɟɪɫɬɢɹ ɮɪɟɡɵ lɲ = 0,3 L .

(2.30)

Ⱦɢɚɦɟɬɪ ɜɵɬɨɱɤɢ ɜ ɨɬɜɟɪɫɬɢɢ dɜ = dɨɬɜ+ 2

(2.3)

ɉɨɫɥɟ ɜɫɟɯ ɪɚɫɱɟɬɨɜ ɫɥɟɞɭɟɬ ɩɪɨɜɟɪɢɬɶ ɭɫɥɨɜɢɹ: 28

ɚ) ɜɨɡɦɨɠɧɨɫɬɢ ɩɟɪɟɬɨɱɟɤ ɢɧɫɬɪɭɦɟɧɬɚ ɛɟɡ ɩɨɜɪɟɠɞɟɧɢɹ ɩɨɜɟɪɯɧɨɫɬɢ ɰɢɥɢɧɞɪɚ ɛɭɪɬɢɤɨɜ; ɛ) ɩɪɨɱɧɨɫɬɢ ɬɟɥɚ ɮɪɟɡɵ ɜ ɦɟɫɬɟ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ. ɚ) [0,5 dao - (0,5d1 + Hk )] ≥ 0,5 ; ɛ) [0,5 dao - (C1 - 0,5dɈɌȼ + Hk )] ≥ 3. ȿɫɥɢ ɷɬɢ ɭɫɥɨɜɢɹ ɧɟ ɜɵɩɨɥɧɹɸɬɫɹ, ɬɨ ɫɥɟɞɭɟɬ ɭɦɟɧɶɲɢɬɶ ɡɧɚɱɟɧɢɹ Ʉ ɢ Ʉ1, ɬ.ɟ. ɇɤ. ɍɦɟɧɶɲɟɧɢɟ ɡɧɚɱɟɧɢɹ Ʉ ɞɨɥɠɧɨ ɨɬɜɟɱɚɬɶ ɬɪɟɛɨɜɚɧɢɸ ɮɨɪɦɭɥɵ 2.8. ȼɩɨɥɧɟ ɜɨɡɦɨɠɧɵɦ ɢ ɰɟɥɟɫɨɨɛɪɚɡɧɵɦ ɹɜɥɹɟɬɫɹ ɭɜɟɥɢɱɟɧɢɟ ɧɚɪɭɠɧɨɝɨ ɞɢɚɦɟɬɪɚ ɢɧɫɬɪɭɦɟɧɬɚ dao. ɉɪɢ ɷɬɨɦ ɫɨɝɥɚɫɧɨ ɬɚɛɥ. 2.. ɫɥɟɞɭɟɬ ɩɟɪɟɣɬɢ ɧɚ ɛɨɥɶɲɟɟ

ɡɧɚɱɟɧɢɟ

dao.

Ɂɚɬɟɦ

ɫɥɟɞɭɟɬ

ɩɟɪɟɫɱɢɬɚɬɶ

ɤɨɧɫɬɪɭɤɬɢɜɧɨ-

ɝɟɨɦɟɬɪɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ ɢɧɫɬɪɭɦɟɧɬɚ ɡɚɧɨɜɨ. 2.2. Ɉɩɪɟɞɟɥɟɧɢɟ ɨɩɬɢɦɚɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɱɢɫɬɨɜɨɣ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɩɪɹɦɨɡɭɛɨɝɨ ɤɨɥɟɫɚ ȼ ɤɚɱɟɫɬɜɟ ɤɪɢɬɟɪɢɹ ɨɩɬɢɦɢɡɚɰɢɢ ɩɪɢɧɹɬɨ ɩɨɜɵɲɟɧɢɟ ɩɟɪɢɨɞɚ ɫɬɨɣɤɨɫɬɢ ɢɧɫɬɪɭɦɟɧɬɚ, ɡɚɜɢɫɹɳɟɝɨ ɨɬ ɜɟɥɢɱɢɧɵ ɡɚɞɧɟɝɨ ɭɝɥɚ ɜ ɦɟɫɬɟ ɫɨɩɪɹɠɟɧɢɹ ɛɨɤɨɜɨɣ ɢ ɜɟɪɲɢɧɨɣ ɪɟɠɭɳɢɯ ɤɪɨɦɨɤ. Ɉɝɪɚɧɢɱɟɧɢɟɦ ɫɥɭɠɢɬ ɬɪɟɛɭɟɦɨɟ ɤɚɱɟɫɬɜɨ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ, ɧɚɪɟɡɚɟɦɵɯ ɫ ɩɨɦɨɳɶɸ ɷɬɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ: ɨɬɫɭɬɫɬɜɢɟ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɩɪɨɮɢɥɟɣ ɡɭɛɶɟɜ ɡɚɰɟɩɥɹɸɳɢɯɫɹ ɤɨɥɟɫ, ɢ, ɟɫɥɢ ɬɪɟɛɭɟɬɫɹ, ɬɨ ɨɬɫɭɬɫɬɜɢɟ ɩɨɞɪɟɡɤɢ ɩɪɨɮɢɥɹ ɭ ɨɫɧɨɜɚɧɢɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ. Ɇɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɭɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɢɡ ɭɫɥɨɜɢɹ ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɨɝɨ ɡɚɞɧɟɝɨ ɭɝɥɚ ɧɚ ɛɨɤɨɜɨɣ ɪɟɠɭɳɟɣ ɤɪɨɦɤɟ α

ωo min

= arcsin

tgα ɛɨɤ . tgα ɜ

(2.32)

ɝɞɟ αɛɨɤ - ɡɚɞɧɢɣ ɭɝɨɥ ɧɚ ɛɨɤɨɜɨɣ ɪɟɠɭɳɟɣ ɤɪɨɦɤɟ. Ɋɟɤɨɦɟɧɞɭɟɬɫɹ αɛɨɤ = 2°30' ÷3°, αɜ = 9°÷12° .

29

ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɩɪɢɧɢɦɚɸɬɫɹ ɡɧɚɱɟɧɢɹ ɭɝɥɚ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɪɟɣɤɢ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ αω0 ɢ ɪɚɞɢɭɫ ɫɨɩɪɹɠɟɧɢɹ ɛɨɤɨɜɨɣ ɢ ɜɟɪɲɢɧɧɨɣ ɪɟɠɭɳɢɯ ɤɪɨɦɨɤ ɪɚɜɧɵɦɢ:

αω0=α; rɝ = 0,2 m.

(2.33)

Ɍɨɝɞɚ ɪɚɞɢɭɫ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ ɩɪɢ ɡɚɰɟɩɥɟɧɢɢ ɟɝɨ ɫ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɨɣ ɫ ɭɝɥɨɦ ɩɪɨɮɢɥɹ αω0 (ɪɢɫ.2.2) rw1 = 0,5 d1⋅ cos α / cosαω0.

(2.34)

ȼɵɫɨɬɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɨɬ ɜɟɪɲɢɧɵ ɡɭɛɶɟɜ ɞɨ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ hn0 = rw1 - 0,5 df1.

(2.35)

ɇɚ ɪɢɫ.2.2 ɫɢɦɜɨɥɵ ɨɛɨɡɧɚɱɚɸɬ ɫɥɟɞɭɸɳɟɟ: rz - ɪɚɞɢɭɫ ɫɨɩɪɹɠɟɧɢɹ ɛɨɤɨɜɨɣ ɢ ɜɟɪɲɢɧɧɨɣ ɪɟɠɭɳɢɯ ɤɪɨɦɨɤ ɡɭɛɨɪɟɡɧɨɣ ɪɟɣɤɢ; rɫɨɩɪ - ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɵɣ ɪɚɞɢɭɫ ɡɚɤɪɭɝɥɟɧɢɹ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ, ɬ.ɟ. ɤɨɝɞɚ ɧɚ ɜɟɪɲɢɧɟ ɡɭɛɶɟɜ ɧɟɬ ɩɪɹɦɨɥɢɧɟɣɧɨɝɨ ɭɱɚɫɬɤɚ; G0 - ɬɨɱɤɚ ɩɟɪɟɯɨɞɚ ɨɬ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɤ ɞɭɝɨɜɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ; G - ɬɨɱɤɚ ɩɟɪɟɯɨɞɚ ɨɬ ɷɜɨɥɶɜɟɧɬɵ ɤ ɩɟɪɟɯɨɞɧɨɣ ɤɪɢɜɨɣ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ. Ɉɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ Y0 Ɋɏ0 ɨɪɞɢɧɚɬɚ ɬɨɱɤɢ G0 - Y0Go, ɤɨɬɨɪɭɸ ɞɥɹ ɤɪɚɬɤɨɫɬɢ ɨɛɨɡɧɚɱɢɦ Y0, ɪɚɜɧɚ: Y0 = [ rz (1 - sin α w0 )] - hn0.

(2.36)

ɒɚɝ ɡɭɛɶɟɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨ ɧɨɪɦɚɥɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ Ɋw0 = 2 πrw1 / z1.

(2.37)

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɮɪɟɡɵ ɩɨ ɧɨɪɦɚɥɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ⎛S ⎞ S n 0 = PW 0 − 2rw ⎜⎜ n + invα − invα W 0 ⎟⎟ . ⎝ mz ⎠

(2.38)

ɉɨɞɪɟɡ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ ɨɬɫɭɬɫɬɜɭɟɬ, ɟɫɥɢ ɜɵɞɟɪɠɢɜɚɟɬɫɹ ɭɫɥɨɜɢɟ: r w ≥

Υ0 . sin 2 α w0

(2.39)

30

Ɋɢɫ. 2.2. ɋɯɟɦɚ ɮɨɪɦɨɨɛɪɚɡɨɜɚɧɢɹ ɷɜɨɥɶɜɟɧɬɧɨɝɨ ɡɭɛɚ.

ȿɫɥɢ ɭɫɥɨɜɢɟ 2.39 ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɚ ɜ ɬɪɟɛɨɜɚɧɢɹɯ ɤ ɡɭɛɱɚɬɨɦɭ ɤɨɥɟɫɭ ɩɨɞɪɟɡ ɡɭɛɚ ɧɟ ɞɨɩɭɫɤɚɟɬɫɹ, ɬɨ ɷɬɨ ɡɧɚɱɢɬ, ɱɬɨ ɫ ɩɨɦɨɳɶɸ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɧɟɨɩɪɟɞɟɥɟɧɧɨɣ ɭɫɬɚɧɨɜɤɢ ɬɚɤɨɟ ɡɭɛɱɚɬɨɟ ɤɨɥɟɫɨ ɢɡɝɨɬɨɜɢɬɶ ɧɟɥɶɡɹ, ɧɚ ɷɬɨɦ ɪɚɫɱɟɬ ɡɚɤɚɧɱɢɜɚɟɬɫɹ. ȿɫɥɢ ɠɟ ɩɨɞɪɟɡ ɞɨɩɭɫɤɚɟɬɫɹ, ɧɨ ɬɨɥɶɤɨ ɧɟ ɧɚ ɪɚɛɨɱɟɣ (ɚɤɬɢɜɧɨɣ) ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ, ɬɨ ɪɚɫɱɟɬ ɩɪɨɞɨɥɠɚɟɬɫɹ. Ɋɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ ɧɚɪɟɡɚɟɦɨɝɨ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɝɪɚɧɢɰɭ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ

3

rp =

(0,5d ⋅ cos α )2 + ρ p 2 .

(2.40)

ɝɞɟ ρp - ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɜ ɬɨɱɤɟ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ, ɩɨɞɫɱɢɬɵɜɚɟɦɨɝɨ ɩɨ ɮɨɪɦɭɥɟ .8. ɍɝɨɥ ɩɪɨɮɢɥɹ ɜ ɬɨɱɤɟ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ α p = arccos

0,5d ⋅ cosα . rp

(2.4)

ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɬɨɱɤɢ ɨɬ ɨɫɢ Y [9], ɫ.24-25, (ɪɢɫ.2.2)

σ p = α w0 − α p .

(2.42)

Ɉɪɞɢɧɚɬɚ ɬɨɱɤɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ, cɨɨɬɜɟɬɫɬɜɭɸɳɟɣ (ɫɨɩɪɹɝɚɟɦɨɣ) ɬɨɱɤɟ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ, ɬ.ɟ. ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɬɨɱɤɢ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ Y0 Ɋɏ0 Y0P = rp ⋅ cos σp – rw1 .

(2.43)

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɮɪɟɡɵ S2 (ɫɦ.ɪɢɫ.2.2), ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɨɛɪɚɛɨɬɤɟ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ Sz= Sn0 - 2 Yop ⋅ tg αw0 .

(2.44)

Ɇɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɵɣ ɞɥɹ ɩɪɢɧɹɬɨɝɨ ɡɧɚɱɟɧɢɹ ɭɝɥɚ ɩɪɨɮɢɥɹ ɪɚɞɢɭɫ ɡɚɤɪɭɝɥɟɧɢɹ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ (ɪɢɫ.2.2)

(0,5S h0 − hh0 ⋅ tgα w0 ) = r ɫɨɩɪ cos α w0 ( − sin α w0 )

.

(2.45)

Ɍɨɥɳɢɧɚ ɡɭɛɚ Sɫɨɩɪ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ rɫɨɩɪ, Sɫɨɩɪ = 2 rɫɨɩɪ ⋅ cos αw0.

(2.46)

Ɉɬɫɭɬɫɬɜɢɟ ɡɚɨɫɬɪɟɧɢɹ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɫɥɨɜɢɟɦ: Sɫɨɩɪ ≥ Sz.

(2.47)

ȿɫɥɢ ɭɫɥɨɜɢɟ 2.47 ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ rz =

(h

h0

+ yop )

− sin α w0

.

(2.48)

ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ rz = rɫɨɩɪ =

S ɫɨɩɪ 2 cosα w0

.

(2.49)

32

ɉɪɢ ɞɨɩɭɫɬɢɦɨɫɬɢ ɩɨɞɪɟɡɚ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ ɫɥɟɞɭɟɬ ɩɪɨɜɟɪɢɬɶ, ɧɟ ɧɚɯɨɞɢɬɫɹ ɥɢ ɨɧ (ɩɨɞɪɟɡ) ɧɚ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ, ɱɬɨ ɧɟɞɨɩɭɫɬɢɦɨ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɫɥɟɞɭɟɬ ɧɚɣɬɢ ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟɫɚ, ɫ

′

ɤɨɬɨɪɨɣ ɧɚɱɢɧɚɟɬɫɹ ɩɨɞɪɟɡ, rp ɢ ɫɪɚɜɧɢɬɶ ɟɝɨ ɫ ɪɚɞɢɭɫɨɦ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟɫɚ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɧɚɱɚɥɭ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ.

′

Ɋɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ rp ɦɨɠɧɨ ɧɚɣɬɢ, ɪɟɲɢɜ ɫɢɫɬɟɦɭ ɬɪɚɧɫɰɟɧɞɟɧɬɧɵɯ ɭɪɚɜɧɟɧɢɣ ɷɜɨɥɶɜɟɧɬɵ ɡɭɛɚ ɤɨɥɟɫɚ

π ⋅ m − S n ⎧ ϕ α = + − invd inv ′ p p′ ⎪⎪ d ⎨ 0,5d cos α ⎪ rp′ = cos d p′ ⎪⎩

(2.50)

ɢ ɩɟɪɟɯɨɞɧɨɣ ɤɪɢɜɨɣ ɫɨɝɥɚɫɧɨ ɜɵɪɚɠɟɧɢɸ 9.5 [9, ɫ.26].

y0 + rw ⎧ = σ arccos ; ⎪ rp′ ⎪ rp′ ⋅ sin σ − (0,5S n 0 + y0 ⋅ tgα w0 ) ⎪ = ψ ; ⎨ r w ⎪ = −ψ . ϕ σ ⎪ p′ ⎪ ⎩ Ɉɛɨɡɧɚɱɢɜ

Ⱥ = invα −

(2.5)

π ⋅ m − S n − invα p′ , ɢ ɡɚɞɚɜɲɢɫɶ α p′ ɜ ɩɪɟɞɟd

ɥɚɯ 0-20° (ɜ ɪɚɞɢɚɧɚɯ 0-0,34906), ɧɚ ɨɫɧɨɜɟ ɚɥɝɨɪɢɬɦɚ ɧɚ ɪɢɫ.2.3 ɢ ɩɪɨɝɪɚɦɦɵ ɞɥɹ ɗȼɆ, ɦɟɬɨɞɨɦ ɢɬɟɪɚɰɢɢ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ȿɫɥɢ

rp

>

α p′ ɢ rp′ .

rp′ ,

(2.52)

ɬɨ ɩɨɞɪɟɡɚ ɧɚ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ ɧɟɬ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɨɜɟɪɹɟɬɫɹ ɭɫɥɨɜɢɟ ɞɨɫɬɚɬɨɱɧɨɫɬɢ ɪɚɫɫɱɢɬɚɧɧɨɝɨ ɡɧɚɱɟɧɢɹ rz ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɦ ɡɧɚɱɟɧɢɟɦ. Ⱦɨɥɠɧɨ ɛɵɬɶ rz ≥ 0,15m.

(2.53)

33

Ɋɢɫ. 2.3. Ⱥɥɝɨɪɢɬɦ ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɞɢɭɫɚ ɨɤɪɭɠɧɨɫɬɢ, ɫ ɤɨɬɨɪɨɣ ɧɚɱɢɧɚɟɬɫɹ ɩɨɞɪɟɡ ɩɪɨɮɢɥɹ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ

ȿɫɥɢ ɭɫɥɨɜɢɹ 2.52 ɢ 2.53 ɧɟ ɜɵɩɨɥɧɹɸɬɫɹ, ɬɨ ɫɥɟɞɭɟɬ ɭɦɟɧɶɲɢɬɶ ɡɧɚɱɟɧɢɟ ɭɝɥɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ αw0 ɧɚ ° ɢ, ɧɚɱɢɧɚɹ ɫ ɮɨɪɦɭɥɵ (2.34), ɩɪɨɢɡɜɟɫɬɢ ɩɟɪɟɪɚɫɱɟɬ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɶɟɜ ɮɪɟɡɵ. ɍɦɟɧɶɲɟɧɢɟ ɭɝɥɚ ɩɪɨɮɢɥɹ αw0 ɦɨɠɧɨ ɩɪɨɢɡɜɨɞɢɬɶ ɞɨ ɡɧɚɱɟɧɢɹ 34

αw0 ≥ αw0 min .

(2.54)

Ɇɨɠɧɨ ɬɚɤɠɟ ɢ ɭɦɟɧɶɲɢɬɶ r2. Ɉɬɫɭɬɫɬɜɢɟ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɩɪɨɮɢɥɟɣ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɜ ɡɚɰɟɩɥɟɧɢɢ ɬɚɤɠɟ ɜɵɪɚɠɚɟɬɫɹ ɭɫɥɨɜɢɟɦ:

rp

>

rp′ .

Ɋɚɫɱɟɬ

rp

(2.55) ɢ

rp′ ɜɵɩɨɥɧɹɟɬɫɹ ɩɨ ɬɟɦ ɠɟ, ɱɬɨ ɢ ɞɥɹ ɩɨɞɪɟɡɚ ɩɪɨɮɢɥɹ ɡɭɛɚ

ɤɨɥɟɫɚ, ɮɨɪɦɭɥɚɦ. ɇɚɢɛɨɥɟɟ ɩɪɨɫɬɨ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ 2.55, ɟɫɥɢ ɭɦɟɧɶɲɢɬɶ ɜɟɥɢɱɢɧɭ rz ɞɨ ɟɝɨ ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɨɝɨ ɡɧɚɱɟɧɢɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɚɫɱɟɬɨɜ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɨɩɬɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɫɥɟɞɭɸɳɢɯ ɩɚɪɚɦɟɬɪɨɜ ɮɪɟɡɵ:

αw0 - ɭɝɥɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ; rz - ɪɚɞɢɭɫɚ ɫɨɩɪɹɠɟɧɢɹ ɛɨɤɨɜɵɯ ɢ ɜɟɪɲɢɧɧɨɣ ɤɪɨɦɤɢ ɡɭɛɚ ɮɪɟɡɵ; hn0 - ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɜɟɪɲɢɧɵ ɡɭɛɚ ɮɪɟɡɵ ɞɨ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ɮɪɟɡɵ; S n0 - ɬɨɥɳɢɧɚ ɡɭɛɚ ɮɪɟɡɵ ɩɨ ɧɨɪɦɚɥɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ. Ʉɪɨɦɟ ɬɨɝɨ, ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɪɚɞɢɭɫ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟɫɚ rw1, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɟɟ ɞɢɚɦɟɬɪ: dw1=2rw1. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɞɚɥɶɧɟɣɲɢɣ ɪɚɫɱɟɬ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɮɪɟɡɵ ɩɪɨɢɡɜɨɞɢɬɶ ɩɨ ɮɨɪɦɭɥɚɦ ɢ ɬɚɛɥɢɰɚɦ ɪɚɡɞɟɥɚ 2 ɢ ɩɨɞɪɚɡɞɟɥɚ 2., ɫɥɟɞɭɟɬ ɨɩɪɟɞɟɥɢɬɶ ɫɥɟɞɭɸɳɢɟ ɜɟɥɢɱɢɧɵ. Ɍɨɥɳɢɧɭ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɩɪɹɦɨɣ ⎞ ⎛ d − d f − hn 0 ⎟⎟ . S t 0 = S n 0 + 2tgα w0 ⎜⎜ 2 ⎠ ⎝

(2.56)

ɉɪɢ αw0 =α, St0 = Sn0 . Ⱦɢɚɦɟɬɪ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɮɪɟɡɵ ɜ ɪɚɫɱɟɬɧɨɦ ɫɟɱɟɧɢɢ Dw =Dt - 2 hn0.

(2.57)

ɍɝɨɥ ɧɚɤɥɨɧɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɧɚ ɧɚɱɚɥɶɧɨɦ ɰɢɥɢɧɞɪɟ

ω = arctg

Dt . Dw ⋅ tgω t

(2.58)

35

Ɉɫɟɜɨɣ ɲɚɝ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɮɪɟɡɵ Px = 0

2πrw i z ⋅ cos ω

(2.59)

Pt 0 i. ɉɪɢ αw0 =α , Px 0 = cos ω t

ɉɪɢɛɥɢɠɟɧɧɨ ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɭɸ ɞɥɢɧɭ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɱɢɫɬɨɜɨɣ ɮɪɟɡɵ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɩɨ ɮɨɪɦɭɥɟ 2.28, ɚ ɬɨɱɧɨ ɩɨ ɮɨɪɦɭɥɟ: lp = [(dɚ1⋅ sinα a1 – dw1⋅ sinα wt0) cosα wt0 ⋅ cosψ ] + PɈɋ.Ɉ .

(2.60)

ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɱɢɫɬɨɜɨɣ ɮɪɟɡɵ ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɤɨɫɨɡɭɛɨɝɨ ɤɨɥɟɫɚ ɫ ɨɩɬɢɦɚɥɶɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɮɪɟɡɵ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɫɥɟɞɭɟɬ ɨɩɪɟɞɟɥɢɬɶ ɩɪɢɜɟɞɟɧɧɨɟ ɱɢɫɥɨ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ ɢ ɫɨɩɪɹɠɟɧɧɨɝɨ ɤɨɥɟɫ ɩɨ ɮɨɪɦɭɥɚɦ: z = z ɩɪɢɜ cos 3 β

ɢ

z

2ɩɪɢɜ

=

z2 . cos 3 β

(2.6)

ȼ ɨɫɬɚɥɶɧɨɦ ɩɚɪɚɦɟɬɪɵ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɪɟɣɤɢ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɞɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ. 2.3. Ɋɚɫɱɟɬ ɪɚɡɦɟɪɨɜ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɩɨɞ ɲɟɜɟɪ Ɉɩɪɟɞɟɥɟɧɢɟ ɧɚɪɭɠɧɨɝɨ ɞɢɚɦɟɬɪɚ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ dɚɨ, ɞɢɚɦɟɬɪɚ ɨɬɜɟɪɫɬɢɹ dɚɬɜ, ɞɥɢɧɵ ɮɪɟɡɵ L, ɤɥɚɫɫɚ ɬɨɱɧɨɫɬɢ, ɱɢɫɥɚ ɡɚɯɨɞɨɜ i, ɱɢɫɥɚ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ z0, ɩɟɪɟɞɧɟɝɨ Ȗɜ ɢ ɡɚɞɧɟɝɨ ɭɝɥɚ Įɜ, ɩɚɞɟɧɢɹ ɡɚɬɵɥɤɚ ɨɫɧɨɜɧɨɝɨ ɡɚɬɵɥɨɜɚɧɢɹ Ʉ, ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɡɚɬɵɥɨɜɚɧɢɹ Ʉ1 ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɨɛɳɟɩɪɢɧɹɬɨɣ ɦɟɬɨɞɢɤɟ, ɢɡɥɨɠɟɧɧɨɣ ɧɚ ɫ. 6–20. Ɂɧɚɱɢɬɟɥɶɧɨ ɨɬɥɢɱɚɟɬɫɹ ɪɚɫɱɟɬ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɮɪɟɡɵ. ɇɚ ɪɢɫ.2.4 ɩɪɟɞɫɬɚɜɥɟɧɵ ɜɚɪɢɚɧɬɵ ɦɨɞɢɮɢɤɚɰɢɢ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɢɦ ɩɪɨɮɢɥɢ ɨɛɪɚɛɨɬɚɧɧɵɯ ɡɭɛɶɟɜ ɤɨɥɟɫ [0]. – Ⱦɥɹ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ m = ÷2 ɦɦ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɧɢɦɚɬɶ ɮɨɪɦɭ Ⱥ. 36

Ⱦɥɹ ɷɬɨɣ ɮɨɪɦɵ Įw0 = 8°40' – 9° ɩɪɢ Į = 20° . – Ⱦɥɹ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ m = 2÷2 ɦɦ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɧɢɦɚɬɶ ɮɨɪɦɭ ȼ. – Ⱦɥɹ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ m = ÷6 ɦɦ ɢɧɨɝɞɚ ɦɨɠɧɨ ɩɪɢɧɢɦɚɬɶ ɮɨɪɦɭ Ȼ. Ⱦɚɥɶɧɟɣɲɢɣ ɪɚɫɱɟɬ ɩɚɪɚɦɟɬɪɨɜ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɮɪɟɡɵ ɨɬɧɨɫɢɬɫɹ ɤ ɮɨɪɦɟ ȼ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɣ ɧɚɢɥɭɱɲɢɟ ɭɫɥɨɜɢɹ ɲɟɜɢɧɝɨɜɚɧɢɹ ɡɭɛɶɟɜ ɤɨɥɟɫ.

Ɋɢɫ. 2.4. Ɏɨɪɦɚ ɡɭɛɶɟɜ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ – ɚ) ɢ ɮɨɪɦɚ ɡɭɛɶɟɜ ɤɨɥɟɫ, ɨɛɪɚɛɨɬɚɧɧɵɯ ɷɬɢɦɢ ɮɪɟɡɚɦɢ – ɛ)

ȼ ɬɚɛɥ. 2.5 ɩɪɢɜɟɞɟɧɵ ɭɝɥɵ ɩɪɨɮɢɥɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɫɥɨɜɢɣ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɧɫɬɪɭɦɟɧɬɚ ɢ ɩɨɜɬɨɪɧɚɹ ɢɧɮɨɪɦɚɰɢɹ ɩɨ ɜɵɛɨɪɭ ɱɢɫɥɚ ɡɚɯɨɞɨɜ ɮɪɟɡɵ i.

37

Ɍɚɛɥɢɰɚ 2.5.

ɉɚɪɚɦɟɬɪɵ ɤɨɥɟɫɚ ɢ ɢɧɫɬɪɭɦɟɧɬɚ

ɑɢɫɥɨ ɡɚɯɨɞɨɜ ɮɪɟɡɵ i ɉɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɤɨɥɟɫɚ ɉɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ

ɍɫɥɨɜɢɹ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɧɫɬɪɭɦɟɧɬɚ ɉɪɟɢɦɭɳɟɉɪɢɦɟɧɟɧɢɟ ɜ ɭɫɥɨɜɢɹɯ ɫɬɜɟɧɧɨɟ ɦɚɫɫɨɜɨɝɨ ɩɪɨɢɡɜɨɞɫɬɜɚ ɩɪɢɦɟɧɟɧɢɟ Ⱦɥɹ ɧɟɱɺɬɧɨ- Ⱦɥɹ ɱɺɬȾɥɹ ɥɸɛɨɝɨ ɝɨ ɱɢɫɥɚ ɧɨɝɨ ɱɢɫɥɚ ɱɢɫɥɚ ɡɭɛɶɟɜ ɡɭɛɶɟɜ ɤɨɥɟ- ɡɭɛɶɟɜ ɤɨɤɨɥɟɫɚ ɫɚ ɥɟɫɚ 2 3 20° 5° 20° 5° 20° 5° 20° 5° 5° 2° 2° 2°

ɉɪɢ df1 < db1 ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ ɧɚɢɦɟɧɶɲɢɣ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɡɭɛɶɟɜ ɮɪɟɡɵ, ɝɚɪɚɧɬɢɪɭɸɳɢɣ ɨɬɫɭɬɫɬɜɢɟ ɩɨɞɪɟɡɚɧɢɹ ɡɭɛɚ ɤɨɥɟɫɚ.

α w0 min = arccos

df

db

.

(2.62)

ȿɫɥɢ ɩɨɞɪɟɡɤɚ ɡɭɛɚ ɤɨɥɟɫɚ ɧɟ ɞɨɩɭɫɤɚɟɬɫɹ, ɬɨ ɞɨɥɠɧɨ ɛɵɬɶ ɜɵɞɟɪɠɚɧɨ ɭɫɥɨɜɢɟ: .

(2.63)

Ɇɨɠɧɨ ɩɪɢɧɹɬɶ α w = α w min . 0 0

(2.64)

α

≥α w 0

w min 0

Ɋɢɫ. 2.5. Ɋɚɡɦɟɪɵ ɡɭɛɶɟɜ ɮɨɪɦɵ ȼ - ɚ) ɢ ɜɚɪɢɚɧɬ ɨɮɨɪɦɥɟɧɢɹ ɭɫɢɤɚ - ɛ)

38

ɉɪɢɩɭɫɤ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ ɫɥɟɞɭɟɬ ɩɪɢɧɹɬɶ ɢɡ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ ɢɡɝɨɬɨɜɥɟɧɢɹ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ ɢɥɢ ɪɚɫɫɱɢɬɚɬɶ ɩɨ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɟ: ǻS = 0,07 m + 0,08.

(2.65)

Ɂɧɚɱɟɧɢɟ ǻS ɨɤɪɭɝɥɢɬɶ ɞɨ ɫɨɬɵɯ ɞɨɥɟɣ ɦɢɥɥɢɦɟɬɪɚ ɜ ɛɨɥɶɲɭɸ ɫɬɨɪɨɧɭ. ɉɪɢɩɭɫɤ ɧɚ ɫɬɨɪɨɧɭ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ ΔS . 2 Ɉɫɧɨɜɧɨɣ ɲɚɝ ɤɨɥɟɫɚ ɢ ɮɪɟɡɵ

δ =

(2.66)

Pb = π ⋅ m ⋅ cos α .

(2.67)

ɒɚɝ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ P

w0

=

P

b cos α

(2.68)

. w

0

ɍɝɨɥ ɧɚɤɥɨɧɚ ɡɭɛɚ ɤɨɥɟɫɚ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ β

w

= arcsin

sin β ⋅ cos α . cos α w 0

(2.69)

ɍɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɮɪɟɡɵ ɢ ɤɨɥɟɫɚ ɜ ɬɨɪɰɨɜɨɣ ɩɥɨɫɤɨɫɬɢ ɤɨɥɟɫɚ tg α

α

wt

= arctg 0

w

(2.70)

0 . cos β w

Ⱦɢɚɦɟɬɪ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟɫɚ d w =

d ⋅ cos α . cos α wt 0

(2.7)

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɧɨɪɦɚɥɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟɫɚ ⎛ S n + ΔS ⎜ S = d ⋅⎜ + inv α − inv α w w t α d β cos ⋅ wt ⎜ 0 ⎝

⎞ ⎟ ⎟. ⎟ ⎠

(2.72)

Ɋɚɫɱɟɬɧɵɟ ɪɚɡɦɟɪɵ ɡɭɛɚ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ: – ɬɨɥɳɢɧɚ ɡɭɛɚ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ɮɪɟɡɵ S n = Pw − S w ; 0 0

(2.73)

39

– ɜɵɫɨɬɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɨɬ ɟɝɨ ɜɟɪɲɢɧɵ ɞɨ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ (ɪɢɫ. 2.6) dw −d f ; hn = 2 0 - ɜɵɫɨɬɚ ɡɭɛɚ ɮɪɟɡɵ

(2.74)

h0 = h + 0,3m .

(2.75)

Ɋɢɫ.2.6. Ɉɩɪɟɞɟɥɟɧɢɟ ɪɚɡɦɟɪɨɜ ɭɫɢɤɨɜ ɡɭɛɚ ɩɪɹɦɨɣ ɮɪɟɡɵ ɜ ɬɨɪɰɨɜɨɣ ɩɥɨɫɤɨɫɬɢ ɤɨɥɟɫɚ

Ɋɚɫɫɬɨɹɧɢɟ ɨɬ ɜɟɪɲɢɧɵ ɡɭɛɚ ɮɪɟɡɵ ɞɨ ɧɚɱɚɥɚ ɭɬɨɥɳɟɧɢɹ (ɪɢɫ.2.6) ⎡⎛ ⎤ ⎞ (2.76) − ⎢ ⎜ 0 ,5 d ⋅ sin α − ρ − δ ⎟ sin α ⎥ ⎜ ⎟ y n w wt p wt ⎥ 0 ⎢⎣ ⎝ 0 0⎦ ⎠ Ɋɚɡɦɟɪɵ ɭɫɢɤɚ ɡɭɛɚ, ɩɪɨɫɬɚɜɥɹɟɦɵɟ ɧɚ ɱɟɪɬɟɠɟ (ɪɢɫ.2.5), ɫɥɟɞɭɸɳɢɟ: h

=h

c=

hy cos α w0

b=c−

;

a = δ + 0 ,05 ;

− 5°)

0,m rz = − sin α

a tg (α

w 0

;

40

(2.77)

. w0

ȿɫɥɢ b < 0,5 ɦɦ, ɬɨ ɩɪɢɧɢɦɚɟɬɫɹ ɮɨɪɦɚ ɭɫɢɤɚ ɩɨ ɪɢɫ.2.5,ɛ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɩɪɢɧɢɦɚɟɬɫɹ ɮɨɪɦɚ ɢ ɪɚɡɦɟɪɵ ɭɫɢɤɚ ɩɨ ɪɢɫ.2.5,ɚ. Ɂɚɬɟɦ ɫɥɟɞɭɟɬ ɩɪɨɜɟɪɢɬɶ ɜɟɥɢɱɢɧɭ ɭɬɨɥɳɟɧɢɹ ɚt ɧɚ ɨɬɫɭɬɫɬɜɢɟ ɱɪɟɡɦɟɪɧɨɝɨ ɩɨɞɪɟɡɚɧɢɹ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ. Ⱦɥɹ ɷɬɨɝɨ ɧɚ ɨɫɧɨɜɚɧɢɢ ɪɢɫ.2.7 ɫɥɟɞɭɟɬ ɩɪɨɢɡɜɟɫɬɢ ɫɥɟɞɭɸɳɢɟ ɪɚɫɱɟɬɵ: - ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ɞɨ ɬɨɱɤɢ, ɩɪɨɢɡɜɨɞɹɳɟɣ ɧɚɢɛɨɥɶɲɭɸ ɩɨɞɪɟɡɤɭ ⎡ h = h − ⎢r k n z 0 ⎢⎣

⎛ ⋅ ⎜ − sin α ⎜ w 0 ⎝

(2.78)

⎞⎤ ⎟ ⎥; ⎟⎥ ⎠⎦

- ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ ɧɚɱɚɥɚ ɚɤɬɢɜɧɨɝɨ ɭɱɚɫɬɤɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ

rȼ =

( 0 ,5 d b ) 2 + ( ρ p + δ ) 2 ;

(2.79)

- ɭɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ ɜ ɬɨɱɤɟ ȼ

α ȼ = arccos

d

(2.80)

b ; 2rɜ

- ɭɝɨɥ Ȝ (ɫɦ. ɪɢɫ.2.7)

λ = arccos

0,5d w − hk rȼ

;

- ɭɝɨɥ ĳ (ɪɢɫ.2.7) (2.8)

ϕ = λ + invα wt 0 − invα ȼ ; - ɜɟɥɢɱɢɧɭ lt (ɪɢɫ.2.7)

⎡ ⎤ ⎞; ɟ = ⎢⎛⎜ 0,5 d − h ⎞⎟ ⋅ tg λ ⎥ − ⎛⎜ 0,5 d ⋅ ϕ − h ⋅ tg α t ⎣⎝ w k⎠ w k wt 0 ⎟⎠ ⎦ ⎝

(2.82)

- ɪɚɡɦɟɪ l (ɧɚ ɪɢɫ.2.7 ɧɟ ɩɨɤɚɡɚɧ)

e = e t ⋅ cos α

wt 0

⋅ cos β w .

4

(2.83)

ȿɫɥɢ ɚ e, ɬɨ ɩɨɞɪɟɡɚɧɢɟ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ ɧɨɪɦɚɥɶɧɨɟ. ȿɫɥɢ a > e, ɬɨ ɫɥɟɞɭɟɬ ɩɪɢɧɹɬɶ ɚ = e ɢ ɩɟɪɟɫɱɢɬɚɬɶ ɪɚɡɦɟɪ b.

Ɋɢɫ. 2.7. ɉɪɨɜɟɪɤɚ ɨɬɫɭɬɫɬɜɢɹ ɩɨɞɪɟɡɚɧɢɹ ɡɭɛɚ ɤɨɥɟɫɚ

Ⱦɥɹ ɨɛɥɟɝɱɟɧɢɹ ɩɪɨɰɟɫɫɚ ɡɭɛɨɲɟɜɢɧɝɨɜɚɧɢɹ ɭ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɫ ɱɢɫɥɨɦ ɡɭɛɶɟɜ z1 >7 ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹ ɮɚɫɤɚ ɭ ɜɟɪɲɢɧɵ ɡɭɛɶɟɜ ɤɨɥɟɫɚ, ɞɥɹ ɢɡɝɨɬɨɜɥɟɧɢɹ ɤɨɬɨɪɨɣ ɧɚ ɡɭɛɟ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹ ɮɥɚɧɤ (ɪɢɫ.2.8). Ɏɚɫɤɚ (ɮɥɚɧɤ) ɧɚ ɡɭɛɱɚɬɨɦ ɤɨɥɟɫɟ ɦɨɠɟɬ ɛɵɬɶ ɡɚɞɚɧɚ ɩɨ-ɪɚɡɧɨɦɭ. ɇɚɩɪɢɦɟɪ, ɲɢɪɢɧɨɣ f ɢ ɭɝɥɨɦ Įɮ. Ɍɨɝɞɚ ɜɵɫɨɬɚ ɮɥɚɧɤɚ hf = f·tgĮɮ. Ɋɚɡɦɟɪɵ ɮɥɚɧɤɚ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɩɨ ɷɦɩɢɪɢɱɟɫɤɢɦ ɡɚɜɢɫɢɦɨɫɬɹɦ: hf = 0,075·m + 0,35; f = 0,05·m.

(2.84)

42

Ɋɢɫ. 2.8. ɋɯɟɦɚ ɤ ɪɚɫɱɟɬɭ ɩɚɪɚɦɟɬɪɨɜ ɮɥɚɧɤɨɜ ɡɭɛɶɟɜ ɮɪɟɡɵ

Ɋɚɫɱɟɬ ɮɥɚɧɤɚ ɧɚ ɡɭɛɟ ɮɪɟɡɵ ɜɪɭɱɧɭɸ ɦɨɠɧɨ ɩɪɨɢɡɜɟɫɬɢ ɩɨ ɫɥɟɞɭɸɳɢɦ ɮɨɪɦɭɥɚɦ. ɍɝɨɥ ɮɥɚɧɤɚ α

ɮ 0

=α

w 0

+ 0°.

(2.85)

Ⱦɢɚɦɟɬɪ ɨɤɪɭɠɧɨɫɬɢ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ, ɫ ɤɨɬɨɪɨɣ ɧɚɱɢɧɚɟɬɫɹ ɮɥɚɧɤ

d A = d a − 2h f

(2.86)

ɍɝɨɥ ɩɪɨɮɢɥɹ ɧɚ ɞɢɚɦɟɬɪɟ dA ɞɥɹ ɨɫɧɨɜɧɨɣ ɷɜɨɥɶɜɟɧɬɵ d

α

A

w = arccos

⋅ cos α d

(2.87)

w 0.

A

ɍɝɨɥ ɩɪɨɮɢɥɹ ɧɚ ɞɢɚɦɟɬɪɟ dA ɞɥɹ ɷɜɨɥɶɜɟɧɬɵ ɮɥɚɧɤɚ d

α

ɮȺ

w = arccos

⋅ cos α d

ɮ 0

(2.88)

A 43

Ɋɚɫɫɬɨɹɧɢɟ ɨɬ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ ɞɨ ɧɚɱɚɥɚ ɮɥɚɧɤɚ d ⋅ (invα − invα − invα + invα ) w A ɮ ɮȺ 0 0 h = + 2h . ɮ n0 2 ⋅ (tgα − tgα ) 0 ɮ w 0 0

(2.89)

Ɂɚɬɟɦ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɜɟɪɢɬɶ ɞɟɣɫɬɜɢɬɟɥɶɧɭɸ ɜɟɥɢɱɢɧɭ ɫɪɟɡɚɧɢɹ ɮɚɫɨɤ ɧɚ ɜɟɪɲɢɧɟ ɡɭɛɚ ɤɨɥɟɫɚ ɢ ɫɪɚɜɧɢɬɶ ɟɟ ɫ ɩɪɢɧɹɬɨɣ ɜɟɥɢɱɢɧɨɣ f. Ⱦɥɹ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɢɡɜɟɫɬɢ ɫɥɟɞɭɸɳɢɟ ɪɚɫɱɟɬɵ. Ɉɩɪɟɞɟɥɢɬɶ ɭɝɨɥ ɩɪɨɮɢɥɹ ɭ ɜɟɪɲɢɧɵ ɡɭɛɚ ɤɨɥɟɫɚ, ɩɨɥɭɱɟɧɧɨɝɨ ɨɬ ɨɫɧɨɜɧɨɣ ɪɟɣɤɢ ɡɭɛɚ ɮɪɟɡɵ. d

α

a

w = arccos ɨɫɧ

⋅ cosα d

w 0.

(2.90)

ɚ

Ɍɨɥɳɢɧɚ ɝɨɥɨɜɤɢ ɡɭɛɚ ɤɨɥɟɫɚ, ɩɨɥɭɱɟɧɧɚɹ ɨɬ ɨɫɧɨɜɧɨɣ ɪɟɣɤɢ S

S

a

=d ɨɫɧ

a

⋅(

w + invα ). − invα w a d ɨɫɧ 0 w

(2.9)

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɤɨɥɟɫɚ ɧɚ ɞɢɚɦɟɬɪɟ dA S

S

A

=d

A

⋅(

w + invα − invα ). w A d 0 w

(2.92)

ɍɝɨɥ ɩɪɨɮɢɥɹ ɧɚ ɝɨɥɨɜɤɟ ɡɭɛɚ ɤɨɥɟɫɚ, ɩɨɥɭɱɚɸɳɟɝɨɫɹ ɨɬ ɪɟɣɤɢ ɮɥɚɧɤɚ d

α

aɮ

w = arccos

⋅ cos α d

w 0.

(2.93)

a

Ɍɨɥɳɢɧɚ ɝɨɥɨɜɤɢ ɡɭɛɚ ɤɨɥɟɫɚ, ɩɨɥɭɱɟɧɧɚɹ ɨɬ ɪɟɣɤɢ ɮɥɚɧɤɚ SȺ + invα ɮȺ − invα ɚɮ ). dȺ

S ɚɮ = d ɚ ⋅ (

(2.94)

ɋɪɟɡ ɝɨɥɨɜɤɢ ɡɭɛɚ ɧɚ ɨɞɧɭ ɫɬɨɪɨɧɭ S q=

a

−S ɨɫɧ 2

ɚɮ

(2.95)

. 44

Ⱦɨɥɠɧɨ ɛɵɬɶ ɜɵɞɟɪɠɚɧɨ ɭɫɥɨɜɢɟ: q § f ɢɥɢ ɧɚ 0,2 ɦɦ ɛɨɥɶɲɟ f.

(2.96)

ɉɪɢ ɪɚɫɱɟɬɟ ɧɚ ɗȼɆ ɜɟɥɢɱɢɧɵ ɮɥɚɧɤɚ Įɮ0 ɢ hɮ0 ɨɩɪɟɞɟɥɹɸɬɫɹ ɛɟɡ ɩɨɝɪɟɲɧɨɫɬɟɣ. ɋɯɟɦɚ ɪɢɫ.2.8 ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɬɨɱɧɵɟ ɮɨɪɦɭɥɵ ɞɥɹ ɪɚɫɱɟɬɚ ɜɟɥɢɱɢɧ Įɮ0 ɢ hɮ0. Ɋɚɞɢɭɫɵ ɤɪɚɣɧɢɯ ɬɨɱɟɤ Ⱥ ɢ ȼ ɮɥɚɧɤɚ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ ɤɨɥɟɫɚ

r

A

= 0,5d

a

−h ; f

r = 0,5d . B a

(2.97)

ɍɝɨɥ ɩɪɨɮɢɥɹ ɜ ɬɨɱɤɟ Ⱥ ɨɫɧɨɜɧɨɣ ɷɜɨɥɶɜɟɧɬɵ 0,5d

α

A

= arccos

w r

⋅ cos α

w 0.

(2.98)

A

ɉɨɥɨɜɢɧɚ ɰɟɧɬɪɚɥɶɧɨɝɨ ɭɝɥɚ ɜɩɚɞɢɧɵ ɦɟɠɞɭ ɡɭɛɶɹɦɢ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ ɤɨɥɟɫɚ, ɨɩɪɟɞɟɥɹɸɳɟɝɨ ɩɨɥɨɠɟɧɢɟ ɬɨɱɤɢ Ⱥ S w π ϕ = − + invα − invα . A w A z d 0 w

(2.99)

ɉɨɥɨɜɢɧɚ ɰɟɧɬɪɚɥɶɧɨɝɨ ɭɝɥɚ ɜɩɚɞɢɧɵ ɦɟɠɞɭ ɡɭɛɶɹɦɢ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ ɤɨɥɟɫɚ, ɨɩɪɟɞɟɥɹɸɳɟɝɨ ɩɨɥɨɠɟɧɢɟ ɬɨɱɤɢ ȼ r

ϕ

B

A =

⋅ϕ

A

+ f

r B

.

(2.00)

Ɋɚɡɧɨɫɬɶ ɷɜɨɥɶɜɟɧɬɧɵɯ ɭɝɥɨɜ ɜ ɬɨɱɤɚɯ Ⱥ ɢ ȼ ɩɪɨɮɢɥɹ ɮɥɚɧɤɚ ɤɨɥɟɫɚ ΔΘ = Θ − Θ = ϕ −ϕ . B A B A

(2.0)

Ɉɩɪɟɞɟɥɹɟɬɫɹ ɪɚɞɢɭɫ ɨɫɧɨɜɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɷɜɨɥɶɜɟɧɬɵ ɮɥɚɧɤɚ rb1' ɢɡ ɭɪɚɜɧɟɧɢɹ ΔΘ = r b′

r r ⎛ 2 ⎞ ⎜ r − r 2 − r 2 − r 2 ⎟ − arccos b′ + arccos b′ . b′ A b′ ⎟ ⎜ B r r ⎠ ⎝ B A

(2.02)

Ɋɟɲɟɧɢɟ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɧɚ ɗȼɆ ɜɵɩɨɥɧɹɟɬɫɹ ɦɟɬɨɞɨɦ ɢɬɟɪɚɰɢɢ ɫ ɬɨɱɧɨɫɬɶɸ 0,0000000.

45

ɍɝɨɥ ɮɥɚɧɤɚ ɧɚ ɮɪɟɡɟ ⎛ 2rb ′ ⋅ cos α w ⎜ 0 d = arccos⎜ ɮ0 ⎜ d ⋅ cos α ⎝

⎞ ⎟ ⎟. ⎟ ⎠

(2.03)

ɍɝɨɥ ɩɪɨɮɢɥɹ ɜ ɬɨɱɤɟ ȼ ɧɚ ɮɥɚɧɤɟ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ ɤɨɥɟɫɚ r b′ α = arccos . B r B

(2.04)

ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɬɨɱɤɢ ȼ ɩɪɢ ɨɛɪɚɛɨɬɤɟ ɨɬ ɨɫɢ Y σ

B

=α

−α

ɮ0

B

(2.05)

.

ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɬɨɱɤɢ ȼ ɩɪɢ ɨɛɪɚɛɨɬɤɟ ɨɬ ɧɚɱɚɥɶɧɨɝɨ ɩɨɥɨɠɟɧɢɹ Ψ

B

=σ

−ϕ

B

B

.

(2.06)

Ʉɨɨɪɞɢɧɚɬɵ ɫɨɩɪɹɠɟɧɧɨɣ ɬɨɱɤɢ ȼ0 ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ Y0ɏ0: Y 0

= r ⋅ cos σ − 0,5d ; B B w

B 0

X0

= rB ⋅ sin σ B − 0,5 d w ⋅ ψ B B0

(2.07)

.

Ⱥɛɫɰɢɫɫɚ ɬɨɱɤɢ Ⱥ0 X

0,5S B n 0 −Y 0 − 0 tgα tgα B ɮ0 w 0 0 . X = 0 A − 0 tgα tgα ɮ0 w 0 0

(2.08)

Ɉɪɞɢɧɚɬɚ ɬɨɱɤɢ Ⱥ0 X Y 0

=

0

−X A 0

0

A 0

B 0 tgα

+Y 0

⋅ tgα B 0

ɮ0

(2.09) .

ɮ0

ȼɵɫɨɬɚ ɮɥɚɧɤɚ h =Y ɮ0 0

A 0

+h . n 0

(2.0)

46

ɍ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɫ m > 4 ɦɦ ɩɨ ɞɧɭ ɜɩɚɞɢɧɵ ɩɪɟɞɭɫɦɚɬɪɢɜɚɸɬ ɤɚɧɚɜɤɭ ɞɥɹ ɜɵɯɨɞɚ ɲɥɢɮɨɜɚɥɶɧɨɝɨ ɤɪɭɝɚ ɩɪɢ ɲɥɢɮɨɜɚɧɢɢ ɩɪɨɮɢɥɹ ɡɭɛɚ (ɪɢɫ.2.9). Ɋɚɡɦɟɪɵ ɤɚɧɚɜɤɢ: hɤɚɧ=–2 ɦɦ, rɤɚɧ= 0,5– ɦɦ. ɒɢɪɢɧɭ ɤɚɧɚɜɤɢ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɨ ɮɨɪɦɭɥɚɦ (2.–2.3). ɒɢɪɢɧɚ ɜɩɚɞɢɧɵ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ɡɭɛɚ ɮɪɟɡɵ π ⋅d S

ɜn.n0

=

Z

w −S

n0

(2.)

.

Ɉɩɪɟɞɟɥɹɟɬɫɹ ɲɢɪɢɧɚ ɜɩɚɞɢɧɵ ɩɨ ɞɧɭ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɮɪɟɡɵ S

ɜn. f

=S

ɜn.n0

− 2 ⋅ (h − h ) ⋅ tgα − 2 ⋅ (h − h ) ⋅ tgα . ɮ0 n0 w ɮ0 ɮ0 0 0

(2.2)

ɒɢɪɢɧɚ ɤɚɧɚɜɤɢ b =S − . ɤɚɧ ɜn. f

(2.3)

ȿɫɥɢ bɤɚɧ < ɦɦ, ɬɨ ɤɚɧɚɜɤɚ ɧɟ ɞɟɥɚɟɬɫɹ, ɚ ɦɟɠɞɭ ɫɬɨɪɨɧɚɦɢ ɮɥɚɧɤɚ ɨɛɪɚɡɭɟɬɫɹ V-ɨɛɪɚɡɧɵɣ ɩɪɨɮɢɥɶ ɫ ɭɝɥɨɦ 2Įɮ0. ȼɵɫɨɬɚ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ h a

=h 0

f

.

(2.4)

ɋɪɟɞɧɢɣ ɪɚɫɱɟɬɧɵɣ ɞɢɚɦɟɬɪ ɮɪɟɡɵ D =d − 2h − (0,4 ÷ 0,5) K . t a a 0 0

(2.5)

Ɉɤɪɭɝɥɹɟɬɫɹ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ 0,0 ɦɦ. ɍɝɨɥ ɧɚɤɥɨɧɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɰɢɥɢɧɞɪɟ m ⋅i ω = arcsin . t D t

(2.6)

Ɂɧɚɱɟɧɢɟ ɩɨɞɫɱɢɬɵɜɚɟɬɫɹ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ 1". ɇɚɩɪɚɜɥɟɧɢɟ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɩɪɚɜɨɟ ɞɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ ɢ ɤɨɫɨɡɭɛɵɯ ɫ ɩɪɚɜɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɡɭɛɶɟɜ. Ⱦɥɹ ɤɨɫɨɡɭɛɵɯ ɤɨɥɟɫ ɫ ɥɟɜɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɡɭɛɶɟɜ ɩɪɢɧɢɦɚɟɬɫɹ ɥɟɜɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ.

47

Ɋɢɫ. 2.9. Ɏɨɪɦɚ ɤɚɧɚɜɤɢ ɧɚ ɞɧɟ ɜɩɚɞɢɧɵ ɦɟɠɞɭ ɡɭɛɶɹɦɢ ɮɪɟɡɵ: m>4ɦɦ; hɤɚɧ = -2 ɦɦ; rɤɚɧ = 0,5-,2 ɦɦ

ȼɵɫɨɬɚ ɡɭɛɚ (ɝɥɭɛɢɧɚ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ) ɮɪɟɡɵ H

=h + k 0

k+k + (0,5 ÷ 2) + h . ɤɚɧ 2

(2.7)

ɇɤ ɨɤɪɭɝɥɹɟɬɫɹ ɫ ɤɪɚɬɧɨɫɬɶɸ ɚ0 = 0,5 ɜ ɛɨɥɶɲɭɸ ɫɬɨɪɨɧɭ. ɍɝɨɥ ɩɪɨɮɢɥɹ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ Ĭ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ 22˚, 25˚, 30˚. Ȼɨɥɶɲɟɟ ɡɧɚɱɟɧɢɟ ɨɛɥɟɝɱɚɟɬ ɩɪɨɰɟɫɫ ɡɚɬɵɥɨɜɚɧɢɹ ɪɟɡɰɨɦ, ɭɜɟɥɢɱɢɜɚɟɬ ɨɛɴɟɦ ɩɪɨɫɬɪɚɧɫɬɜɚ ɞɥɹ ɪɚɡɦɟɳɟɧɢɹ ɫɬɪɭɠɤɢ. Ɋɚɞɢɭɫ ɡɚɤɪɭɝɥɟɧɢɹ ɜ ɨɫɧɨɜɚɧɢɢ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ r = π ⋅ (d

a

0

− 2 H ) / 0 Z . k 0

(2.8)

Ɂɧɚɱɟɧɢɟ r ɨɤɪɭɝɥɢɬɶ ɫ ɤɪɚɬɧɨɫɬɶɸ 0,5. ɉɨ ɦɟɬɨɞɢɤɟ, ɢɡɥɨɠɟɧɧɨɣ ɧɚ ɫ. 2–23, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɞɨɫɬɚɬɨɱɧɨɫɬɶ ɞɥɢɧɵ ɩɪɨɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɡɚɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɡɭɛɚ ɮɪɟɡɵ. ɇɚɩɪɚɜɥɟɧɢɟ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɨɪɦɚɥɶɧɨɟ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɮɪɟɡɵ, ɬ.ɟ. ɭɝɨɥ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ

ω =ω . k t

(2.9)

48

Ɍɨɝɞɚ ɨɫɟɜɨɣ ɲɚɝ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ π ⋅D t. P = z tgω k

(2.20)

ɉɪɢ Ȧt < 3˚ ɦɨɠɧɨ ɢɡɝɨɬɚɜɥɢɜɚɬɶ ɩɪɹɦɵɟ ɫɬɪɭɠɟɱɧɵɟ ɤɚɧɚɜɤɢ, ɬ.ɟ. Ȧk = 0 ɢ Ɋz = . Ⱦɢɚɦɟɬɪ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɮɪɟɡɵ ɜ ɪɚɫɱɟɬɧɨɦ ɫɟɱɟɧɢɢ D

w 0

=d

a

(2.2)

− 2h − (0,4 ÷ 0,5) K . n 0 0

ɡɞɟɫɶ ɢɡ ɤɨɷɮɮɢɰɢɟɧɬɨɜ 0,4-0,5 ɩɪɢɧɢɦɚɟɬɫɹ ɬɚɤɨɣ ɠɟ, ɤɚɤ ɢ ɜ 2.4. ɍɝɨɥ ɧɚɤɥɨɧɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɧɚ ɧɚɱɚɥɶɧɨɦ ɰɢɥɢɧɞɪɟ ⎛ ⎞ ⎜ D ⎟ ω = arctg ⎜ t ⋅ tgω ⎟. t⎟ ⎜⎜ Dw ⎟ 0 ⎝ ⎠

(2.22)

ɒɚɝ ɜɢɬɤɨɜ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɩɨ ɨɫɢ ɮɪɟɡɵ P w 0 . P = x 0 cos ω

(2.23)

ɍɝɨɥ ɭɫɬɚɧɨɜɤɢ ɮɪɟɡɵ ɧɚ ɫɬɚɧɤɟ

ψ = β ±ω . (2.24) t Ɂɧɚɤ «+» ɛɟɪɟɬɫɹ ɩɪɢ ɪɚɡɧɨɢɦɟɧɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ ɜɢɬɤɨɜ ɮɪɟɡɵ ɢ ɡɭɛɶɟɜ ɤɨɥɟɫɚ, « - » – ɩɪɢ ɨɞɧɨɢɦɟɧɧɵɯ. ɉɪɨɮɢɥɢɪɨɜɚɧɢɟ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɩɨɞ ɲɟɜɟɪ ɩɪɨɢɡɜɨɞɢɬɫɹ ɧɚ ɨɫɧɨɜɟ ɤɨɧɜɨɥɸɬɧɨɝɨ ɱɟɪɜɹɤɚ, ɢ ɩɨɷɬɨɦɭ ɧɚ ɪɚɛɨɱɟɦ ɱɟɪɬɟɠɟ ɢɧɫɬɪɭɦɟɧɬɚ ɞɨɫɬɚɬɨɱɧɨ ɩɨɤɚɡɚɬɶ ɩɪɨɮɢɥɶ ɢ ɪɚɡɦɟɪɵ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɜ ɧɨɪɦɚɥɶɧɨɦ ɤ ɜɢɬɤɚɦ ɫɟɱɟɧɢɢ. Ⱦɥɹ ɮɪɟɡ ɫ ɭɦɟɧɶɲɟɧɧɵɦ ɭɝɥɨɦ ɩɪɨɮɢɥɹ Įwo < 20˚ ɩɪɢ ɜɟɥɢɱɢɧɟ Įɛ < 2˚ 30' ɩɪɨɢɡɜɨɞɢɬɫɹ ɤɨɫɨɟ ɡɚɬɵɥɨɜɚɧɢɟ ɩɨɞ ɭɝɥɨɦ Ĳ=30˚. Ⱥ ɭɝɨɥ Įɛ ɩɨɞɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ: ⎡ ⎞⎤ ⎛ α = arctg ⎢tgα ⋅ sin ⎜ α + τ ⎟⎥. ⎟⎥ ⎜ w ɛ ⎢⎣ ɜ ⎠⎦ ⎝ 0

49

ɒɚɝ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɩɪɹɦɨɣ P = π ⋅ m. (2.25) t0 Ɍɨɥɳɢɧɚ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɩɪɹɦɨɣ S

t

=S 0

n 0

+ 2tgα

w 0

(h − h ). a n 0 0

(2.26)

ɒɚɝ ɦɟɠɞɭ ɫɨɫɟɞɧɢɦɢ ɩɪɨɮɢɥɹɦɢ ɩɨ ɨɫɢ ɮɪɟɡɵ P w 0 . P = oc.0 cos ω

(2.27)

Ɍɨɥɳɢɧɚ ɡɭɛɶɟɜ ɜ ɨɫɟɜɨɦ ɫɟɱɟɧɢɢ ɮɪɟɡɵ ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɞɢɚɦɟɬɪɟ S S

oc.0

=

t

0 . cos ω t

(2.28)

ɉɪɨɜɟɪɤɚ ɞɨɫɬɚɬɨɱɧɨɫɬɢ ɩɪɢɧɹɬɨɣ ɞɥɢɧɵ ɮɪɟɡɵ, ɨɩɪɟɞɟɥɟɧɢɟ ɞɢɚɦɟɬɪɚ ɢ ɞɥɢɧɵ ɛɭɪɬɢɤɨɜ, ɪɚɡɦɟɪɨɜ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ ɜ ɩɨɫɚɞɨɱɧɨɦ ɨɬɜɟɪɫɬɢɢ, ɞɥɢɧ ɩɪɨɲɥɢɮɨɜɚɧɧɵɯ ɱɚɫɬɟɣ ɢ ɜɵɬɨɱɤɢ ɜ ɩɨɫɚɞɨɱɧɨɦ ɨɬɜɟɪɫɬɢɢ, ɪɚɡɦɟɪɨɜ ɡɚɛɨɪɧɨɝɨ ɤɨɧɭɫɚ (ɩɪɢ ɟɝɨ ɧɟɨɛɯɨɞɢɦɨɫɬɢ) ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɜɵɲɟɢɡɥɨɠɟɧɧɵɦ ɦɟɬɨɞɢɤɚɦ. 2.4. Ɉɫɨɛɟɧɧɨɫɬɢ ɪɚɫɱɟɬɚ ɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɞɥɹ ɢɡɝɨɬɨɜɥɟɧɢɹ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɫ ɷɜɨɥɶɜɟɧɬɧɵɦ ɩɪɨɮɢɥɟɦ ɡɭɛɶɟɜ Ɍɟɯɧɨɥɨɝɢɹ ɢɡɝɨɬɨɜɥɟɧɢɹ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɫ ɷɜɨɥɶɜɟɧɬɧɵɦ ɩɪɨɮɢɥɟɦ ɲɥɢɰɟɜ ɡɚɜɢɫɢɬ ɨɬ ɬɢɩɚ ɩɪɨɢɡɜɨɞɫɬɜɚ, ɬɟɪɦɢɱɟɫɤɨɣ ɨɛɪɚɛɨɬɤɢ ɞɟɬɚɥɟɣ, ɜɢɞɚ ɰɟɧɬɪɢɪɨɜɚɧɢɹ ɞɟɬɚɥɟɣ ɲɥɢɰɟɜɨɝɨ ɫɨɟɞɢɧɟɧɢɹ: ɩɨ ɧɚɪɭɠɧɨɦɭ, ɜɧɭɬɪɟɧɧɟɦɭ ɞɢɚɦɟɬɪɭ ɜɚɥɚ, ɩɨ ɩɪɨɮɢɥɸ ɲɥɢɰɟɜ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɧɤɪɟɬɧɵɯ ɭɫɥɨɜɢɣ ɩɪɨɢɡɜɨɞɫɬɜɚ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɞɥɹ ɢɯ ɨɛɪɚɛɨɬɤɢ ɩɪɢɦɟɧɹɸɬɫɹ ɱɟɪɜɹɱɧɵɟ ɱɟɪɧɨɜɵɟ ɢ ɱɢɫɬɨɜɵɟ ɮɪɟɡɵ, ɱɟɪɜɹɱɧɵɟ ɮɪɟɡɵ ɩɨɞ ɩɨɫɥɟɞɭɸɳɟɟ ɲɥɢɮɨɜɚɧɢɟ ɢ ɲɟɜɢɧɝɨɜɚɧɢɟ. Ɍɚɤ ɤɚɤ ɲɥɢɰɟɜɵɟ ɜɚɥɵ ɫ ɷɜɨɥɶɜɟɧɬɧɵɦɢ ɡɭɛɶɹɦɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ ɧɟ ɨɬɥɢɱɚɸɬɫɹ ɨɬ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɫ ɷɜɨɥɶɜɟɧɬɧɵɦɢ ɡɭɛɶɹɦɢ, ɬɨ ɪɚɫɱɟɬ ɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɞɥɹ ɬɚɤɢɯ ɜɚɥɨɜ ɜ ɩɪɢɧɰɢɩɟ ɧɟ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɩɪɨ50

ɟɤɬɢɪɨɜɚɧɢɹ ɱɟɪɜɹɱɧɵɯ ɡɭɛɨɪɟɡɧɵɯ ɮɪɟɡ, ɢ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɜɟɞɟɧ ɩɨ ɦɟɬɨɞɢɤɚɦ, ɢɡɥɨɠɟɧɧɵɦ ɜ ɪɚɡɞɟɥɟ 2 (ɩɨɞɪɚɡɞɟɥɵ 2.–2.3). Ʉɚɤ ɩɪɚɜɢɥɨ, ɭɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ Įw0 ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ ɭɝɥɭ ɩɪɨɮɢɥɹ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ Į. Ɇɨɠɟɬ ɛɵɬɶ ɭɜɟɥɢɱɟɧ ɭɝɨɥ ɧɚɤɥɨɧɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ Ȧt ɞɨ 3÷5˚. Ɉɛɵɱɧɨ ɬɪɟɛɭɟɬɫɹ ɩɪɨɟɤɬɢɪɨɜɚɬɶ ɨɞɧɨɡɚɯɨɞɧɵɟ ɮɪɟɡɵ, ɬ.ɤ. ɨɧɢ ɨɛɟɫɩɟɱɚɬ ɛɨɥɶɲɭɸ ɬɨɱɧɨɫɬɶ ɨɤɪɭɠɧɨɝɨ ɲɚɝɚ ɲɥɢɰɟɜ ɜɚɥɚ. Ɍɚɤ ɤɚɤ Įw0 = Į, ɬɨ ɧɚɱɚɥɶɧɚɹ ɩɪɹɦɚɹ ɢ ɞɟɥɢɬɟɥɶɧɚɹ ɩɪɹɦɚɹ ɫɨɜɩɚɞɭɬ, ɢ ɬɨɥɳɢɧɚ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ St = Sn0, ɚ ɮɨɪɦɭɥɚ 2.76 ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɱɟɪɜɹɱɧɨ-ɲɥɢɰɟɜɵɦ ɮɪɟɡɚɦ ɛɭɞɟɬ ɢɦɟɬɶ ɜɢɞ: h = h − (0,5d ⋅ sin α − ρ − δ ) ⋅ sin α . y a w p w 0 0 0

(2.29)

ɝɞɟ ȡp – ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɷɜɨɥɶɜɟɧɬɵ ɜ ɬɨɱɤɟ ɩɪɨɮɢɥɹ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɧɚɱɚɥɨ ɤɨɧɬɚɤɬɚ ɩɪɨɮɢɥɟɣ ɜɚɥɚ ɢ ɜɬɭɥɤɢ, ɪɚɫɫɱɢɬɵɜɚɟɦɨɝɨ ɩɨ ɮɨɪɦɭɥɟ .29.

2.5. Ⱦɨɩɨɥɧɢɬɟɥɶɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɪɚɡɪɚɛɨɬɤɢ ɪɚɛɨɱɟɝɨ ɱɟɪɬɟɠɚ ɡɭɛɨɪɟɡɧɨɣ ɮɪɟɡɵ Ɋɚɛɨɱɢɣ ɱɟɪɬɟɠ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɜɵɩɨɥɧɹɟɬɫɹ ɜ ɦɚɫɲɬɚɛɟ :. ȼɢɞɵ, ɪɚɡɪɟɡɵ, ɫɟɱɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɵ ɜ ɛóɥɶɲɟɦ ɦɚɫɲɬɚɛɟ. Ɏɪɟɡɵ ɢɡɝɨɬɚɜɥɢɜɚɸɬɫɹ ɢɡ ɛɵɫɬɪɨɪɟɠɭɳɢɯ ɫɬɚɥɟɣ ɦɚɪɨɤ Ɋ6Ɇ5, Ɋ6Ɇ5Ʉ5, Ɋ9Ʉ5, Ɋ9Ʉ0, Ɋ4Ɏ4 ȽɈɋɌ 9265–73. ɉɪɢɦɟɧɟɧɢɟ ɦɚɪɤɢ ɫɬɚɥɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɨɛɪɚɛɚɬɵɜɚɟɦɵɦ ɦɚɬɟɪɢɚɥɨɦ ɢ ɬɢɩɨɦ ɩɪɨɢɡɜɨɞɫɬɜɚ. ɒɟɪɨɯɨɜɚɬɨɫɬɶ ɩɨɜɟɪɯɧɨɫɬɢ ɱɟɪɜɹɱɧɵɯ ɡɭɛɨɪɟɡɧɵɯ ɮɪɟɡ ɡɚɜɢɫɢɬ ɨɬ ɤɥɚɫɫɚ ɢɯ ɬɨɱɧɨɫɬɢ ɢ ɦɨɠɟɬ ɛɵɬɶ ɧɚɡɧɚɱɟɧɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 2.6.

5

Ɍɚɛɥɢɰɚ 2.6. Ʉɥɚɫɫɵ ɬɨɱɧɨɫɬɢ ɮɪɟɡɵ Ⱥ ȼ Ɇɨɞɭɥɶ m, ɦɦ

ȺȺ ɇɚɢɦɟɧɨɜɚɧɢɟ ɩɨɜɟɪɯɧɨɫɬɟɣ

ɋ

–

3,5

ɋɜ

–

3,5

ɋɜ

–

3,5

0–

–

3,5

0–

3,5

–0 0–

3,5

–0 0–

3,5

–0

25

3,5

–0

25

25

25

ɒɟɪɨɯɨɜɚɬɨɫɬɶ Ra, ɦɤɦ ɉɨɫɚɞɨɱɧɨɟ ɨɬɜɟɪɫɬɢɟ ɉɟɪɟɞɧɹɹ ɩɨɜɟɪɯɧɨɫɬɶ Ɂɚɞɧɹɹ ɛɨɤɨɜɚɹ ɩɨɜɟɪɯɧɨɫɬɶ Ɂɚɞɧɹɹ ɩɨɜɟɪɯɧɨɫɬɶ ɧɚ ɜɟɪɲɢɧɟ ɡɭɛɚ ɐɢɥɢɧɞɪɢɱɟɫɤɚɹ ɩɨɜɟɪɯɧɨɫɬɶ ɛɭɪɬɢɤɚ Ɍɨɪɟɰ ɛɭɪɬɢɤɚ

0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,8 0,8 0,8 0,8 0,8 0,4 0,4 0,4 0,8 0,8 0,8 0,8 0,8 ,6 ,6 ,6 ,6 0,4 0,4 0,8 0,4 0,4 0,8 0,8 0,8 ,6 ,6 ,6 ,6 0,4 0,4 0,8 0,8 0,8 0,8 0,8 0,8 ,6 ,6 ,6 ,6 0,4 0,4 0,8 0,4 0,4 0,8 0,8 0,8 ,6 ,6 ,6 ,6 0,4 0,4 0,8 0,4 0,4 0,8 0,8 0,8 ,6 ,6 ,6 ,6

ȼ ɩɪɚɜɨɦ ɜɟɪɯɧɟɦ ɭɝɥɭ ɱɟɪɬɟɠɚ ɭɤɚɡɵɜɚɟɬɫɹ ɲɟɪɨɯɨɜɚɬɨɫɬɶ Ra 2,5, ɤɪɨɦɟ ɬɟɯ ɩɨɜɟɪɯɧɨɫɬɟɣ, ɧɚ ɤɨɬɨɪɵɯ ɧɚ ɱɟɪɬɟɠɟ ɞɨɥɠɧɚ ɛɵɬɶ ɩɪɨɫɬɚɜɥɟɧɚ ɲɟɪɨɯɨɜɚɬɨɫɬɶ ɜ ɦɢɤɪɨɦɟɬɪɚɯ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 2.6. ɉɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɩɨ ɧɚɪɭɠɧɨɦɭ ɞɢɚɦɟɬɪɭ, ɞɢɚɦɟɬɪɭ ɛɭɪɬɢɤɨɜ ɢ ɨɛɳɟɣ ɞɥɢɧɟ – h 6. ɉɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɞɪɭɝɢɯ ɪɚɡɦɟɪɨɜ ɮɪɟɡɵ ɞɨɥɠɧɵ ɛɵɬɶ ɧɟ ɛɨɥɟɟ ɭɤɚɡɚɧɧɵɯ ɜ ɬɚɛɥ. 2.4, 2.7, 2.8.

52

Ɍɚɛɥɢɰɚ 2.7. ɇɚɢɦɟɧɨɜɚɧɢɟ ɩɚɪɚɦɟɬɪɚ

Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ Ⱥ ȼ ɋ

Ⱦɢɚɦɟɬɪ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ

Ⱦɨɩɭɫɤ ɇ5 ɇ6 ɇ6 ɇ7 Ɍɚɛɥɢɰɚ 2.8.

ɇɚɢɦɟɧɨɜɚɧɢɟ ɩɚɪɚɦɟɬɪɚ

Ɍɨɥɳɢɧɚ ɡɭɛɚ

Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ Ⱥ ȼ ɋ

Ɇɨɞɭɥɶ, ɦɦ –2

-6 -25 -32 -50

ɋɜ. 2– 3,5

ɋɜ. 3,5–6

ɋɜ. 6– 0

ɋɜ. 0–6

ɋɜ. 6–25

ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ, ɦɤɦ -20 -25 -32 -40 -32 -40 -50 -63 -40 -50 -63 -80 -63 -80 -00 -25

-50 -80 -00 -60

ɇɚ ɪɚɛɨɱɟɦ ɱɟɪɬɟɠɟ ɩɪɢ ɩɨɦɨɳɢ ɭɫɥɨɜɧɵɯ ɨɛɨɡɧɚɱɟɧɢɣ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ȽɈɋɌ 2.308-79 ɞɨɥɠɧɵ ɛɵɬɶ ɭɤɚɡɚɧɵ: ɪɚɞɢɚɥɶɧɨɟ ɛɢɟɧɢɟ ɛɭɪɬɢɤɨɜ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 2.9: Ɍɚɛɥɢɰɚ 2.9. ɇɚɢɦɟɧɨɜɚɧɢɟ ɨɬɤɥɨɧɟɧɢɹ

Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ

–2

Ɋɚɞɢɚɥɶɧɨɟ ɛɢɟɧɢɟ ɛɭɪɬɢɤɨɜ

ȺȺ Ⱥ ȼ ɋ

5 5 6 0

Ɇɨɞɭɥɶ, ɦɦ ɋɜ. 2– ɋɜ. ɋɜ. 6– ɋɜ. 3,5 3,5–6 0 0–6 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ, ɦɤɦ 5 5 5 6 5 6 8 0 8 0 2 6 2 6 20 20

ɋɜ. 6–25 8 2 6 20

ɬɨɪɰɨɜɨɟ ɛɢɟɧɢɟ ɛɭɪɬɢɤɨɜ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 2.0: Ɍɚɛɥɢɰɚ 2.0. ɇɚɢɦɟɧɨɜɚɧɢɟ ɨɬɤɥɨɧɟɧɢɹ


–2

Ɍɨɪɰɟɜɨɟ ɛɢɟɧɢɟ ɛɭɪɬɢɤɨɜ

ȺȺ Ⱥ ȼ ɋ

3 3 4 8

Ɇɨɞɭɥɶ, ɦɦ ɋɜ. 2– ɋɜ. ɋɜ. 6– ɋɜ. 3,5 3,5–6 0 0–6 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ, ɦɤɦ 3 4 5 5 4 5 6 8 5 6 8 0 0 2 6 6 53

ɋɜ. 6–25 6 0 2 6

ɪɚɞɢɚɥɶɧɨɟ ɛɢɟɧɢɟ ɩɨ ɜɟɪɲɢɧɚɦ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 2.: Ɍɚɛɥɢɰɚ 2.. ɇɚɢɦɟɧɨɜɚɧɢɟ ɨɬɤɥɨɧɟɧɢɹ


–2

Ɋɚɞɢɚɥɶɧɨɟ ɛɢɟɧɢɟ ɩɨ ɜɟɪɲɢɧɚɦ ɡɭɛɶɟɜ

ȺȺ Ⱥ ȼ ɋ

2 20 32 50

Ɇɨɞɭɥɶ, ɦɦ ɋɜ. 2– ɋɜ. ɋɜ. 6– ɋɜ. 3,5 3,5–6 0 0–6 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ, ɦɤɦ 6 20 25 32 25 32 40 60 40 50 63 80 63 80 00 25

ɋɜ. 6–25 40 63 00 60

ɋɥɨɜɚ «Ɍɟɯɧɢɱɟɫɤɢɟ ɬɪɟɛɨɜɚɧɢɹ» ɧɟ ɩɢɲɭɬɫɹ, ɩɨɪɹɞɤɨɜɵɣ ɧɨɦɟɪ ɬɪɟɛɨɜɚɧɢɣ ɞɨɥɠɟɧ ɧɚɯɨɞɢɬɶɫɹ ɧɚ ɭɪɨɜɧɟ 2 ɫɦ ɨɬ ɥɟɜɨɣ ɫɬɨɪɨɧɵ ɲɬɚɦɩɚ ɱɟɪɬɟɠɚ, ɚ ɩɪɨɞɨɥɠɟɧɢɟ ɬɟɤɫɬɚ ɬɪɟɛɨɜɚɧɢɹ ɧɚ ɭɪɨɜɧɟ ɥɟɜɨɣ ɫɬɨɪɨɧɵ ɲɬɚɦɩɚ ɱɟɪɬɟɠɚ: ȼ ɬɟɯɧɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɹɯ ɞɨɥɠɧɨ ɛɵɬɶ ɭɤɚɡɚɧɨ: . HRCɷ 63...65. 2. ɇɚ ɜɫɟɯ ɩɨɜɟɪɯɧɨɫɬɹɯ ɮɪɟɡ ɧɟ ɞɨɥɠɧɨ ɛɵɬɶ ɬɪɟɳɢɧ, ɡɚɭɫɟɧɰɟɜ ɢ ɫɥɟɞɨɜ ɤɨɪɪɨɡɢɢ. 3. ɇɟɩɨɥɧɵɟ ɜɢɬɤɢ ɩɪɢɬɭɩɢɬɶ ɞɨ ɬɨɥɳɢɧɵ ɜɟɪɯɧɟɣ ɱɚɫɬɢ ɡɭɛɚ ɧɟ ɦɟɧɟɟ 0,5 ɦɨɞɭɥɹ. 4. ɉɪɹɦɨɥɢɧɟɣɧɨɫɬɶ ɢ ɧɚɤɥɨɧ ɥɢɧɢɢ ɩɟɪɟɫɟɱɟɧɢɹ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɩɥɨɫɤɨɫɬɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɨɫɢ ɮɪɟɡɵ, ɧɚ ɪɚɛɨɱɟɣ ɜɵɫɨɬɟ ɡɭɛɚ (ɬɚɛɥ. 2.2). Ɍɚɛɥɢɰɚ 2.2 Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ

–2

ȺȺ Ⱥ ȼ ɋ

0,02 0,02 0,02 0,25

Ɇɨɞɭɥɶ, ɦɦ ɋɜ. 2–3,5 ɋɜ. 3,5–6 ɋɜ. 6–0

ɋɜ. 0– 6 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ, ɦɦ 0,06 0,02 0,025 0,032 0,025 0,032 0,04 0,05 0,04 0,05 0,063 0,08 0,6 0,02 0,025 0,35

54

ɋɜ. 6– 25 0,04 0,063 0, 0,04

5. ɇɚɤɨɩɥɟɧɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɨɤɪɭɠɧɨɝɨ ɲɚɝɚ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ (ɬɚɛɥ. 2.3) Ɍɚɛɥɢɰɚ 2.3 Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ

–2

ȺȺ Ⱥ ȼ ɋ

0,025 0,04 0,063 0,25

Ɇɨɞɭɥɶ, ɦɦ ɋɜ. 2–3,5 ɋɜ. 3,5–6 ɋɜ. 6–0

ɋɜ. 0– 6 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ, ɦɦ 0,032 0,04 0,05 0,063 0,05 0,063 0,08 0, 0,08 0, 0,25 0,6 0,6 0,2 0,25 0,35

ɋɜ. 6– 25 0,08 0,25 0,2 0,4

6. Ɉɬɤɥɨɧɟɧɢɟ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬ ɧɨɦɢɧɚɥɶɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ, ɨɬɧɟɫɟɧɧɨɟ ɤ 00 ɦɦ ɞɥɢɧɵ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɮɪɟɡɵ (ɬɚɛɥ. 2.4) Ɍɚɛɥɢɰɚ 2.4 Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ

Ɇɨɞɭɥɶ, ɦɦ Ɉɬ ɞɨ 0 ɋɜ. 0 ɞɨ 25 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ, ɦɦ + 0,063 + 0,05 + 0,08 + 0,07 + 0, + 0,25

ȺȺ Ⱥ ȼ ɋ

7. ɉɨɝɪɟɲɧɨɫɬɶ ɡɚɰɟɩɥɟɧɢɹ ɨɬ ɡɭɛɚ ɞɨ ɡɭɛɚ (ɬɚɛɥ. 2.5) Ɍɚɛɥɢɰɚ 2.5 Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ

–2

ȺȺ Ⱥ ȼ ɋ

0,004 0,006 0,0 0,06

Ɇɨɞɭɥɶ, ɦɦ ɋɜ. 2–3,5 ɋɜ. 3,5–6 ɋɜ. 6–0


8. ɉɨɝɪɟɲɧɨɫɬɶ ɡɚɰɟɩɥɟɧɢɹ (ɬɚɛɥ. 2.6)

55

ɋɜ. 6– 25 0,2 0,02 0,032 0,05

Ɍɚɛɥɢɰɚ 2.6 Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ

–2

ȺȺ Ⱥ ȼ ɋ

0,008 0,02 0,06 0,032

Ɇɨɞɭɥɶ, ɦɦ ɋɜ. 2–3,5 ɋɜ. 3,5–6 ɋɜ. 6–0


ɋɜ. 6– 25 0,025 0,040 0,063 0,00

9. ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ɞɨɥɠɧɨ ɛɵɬɶ ɜɵɞɟɪɠɚɧɨ ɧɚ 60% ɞɥɢɧɵ ɤɚɠɞɨɝɨ ɩɨɫɚɞɨɱɧɨɝɨ ɩɨɹɫɤɚ. 0. Ⱦɨɩɭɫɤɚɟɦɨɟ ɫɦɟɳɟɧɢɟ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜ. (ɫɦ. ɬɚɛɥ. 2.4). . ɇɟɭɤɚɡɚɧɧɵɟ ɩɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɪɚɡɦɟɪɨɜ: ɨɬɜɟɪɫɬɢɣ ɇ14, ɜɚɥɨɜ – h14, ɨɫɬɚɥɶɧɵɯ ± IT16/2. 2. Ɇɚɪɤɢɪɨɜɚɬɶ: m = ... Į = ... ɤɥ.... Ȧt = ... Ɋz =... Ɋ6Ɇ5 (ɢɥɢ ɞɪɭɝɚɹ ɦɚɪɤɚ ɫɬɚɥɢ).

56

3. ɊȺɋɑȿɌ ɂ ɉɊɈȿɄɌɂɊɈȼȺɇɂȿ ɋɊȿȾɇȿɆɈȾɍɅɖɇɕɏ ȾɈɅȻəɄɈȼ 3.1. Ɉɩɪɟɞɟɥɟɧɢɟ ɱɢɫɥɚ ɡɭɛɶɟɜ ɢ ɢɫɯɨɞɧɨɝɨ ɪɚɫɫɬɨɹɧɢɹ ɡɭɛɨɪɟɡɧɨɝɨ ɞɨɥɛɹɤɚ ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɱɢɫɥɚ ɡɭɛɶɟɜ ɭɱɢɬɵɜɚɸɬ ɫɬɨɢɦɨɫɬɶ ɞɨɥɛɹɤɚ – ɫɥɨɠɧɨɝɨ ɢ ɞɨɪɨɝɨɝɨ ɪɟɠɭɳɟɝɨ ɢɧɫɬɪɭɦɟɧɬɚ, – ɤɨɬɨɪɚɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɱɢɫɥɚ ɡɭɛɶɟɜ ɪɚɫɬɟɬ. ɉɪɢ ɧɚɪɟɡɚɧɢɢ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɜɧɟɲɧɟɝɨ ɡɚɰɟɩɥɟɧɢɹ ɞɨɥɛɹɤɨɦ ɜɨɡɦɨɠɧɵ ɬɪɢ ɜɢɞɚ ɢɧɬɟɪɮɟɪɟɧɰɢɢ: ɫɪɟɡ ɝɨɥɨɜɤɢ ɡɭɛɚ ɤɨɥɟɫɚ ɩɟɪɟɯɨɞɧɨɣ ɤɪɢɜɨɣ ɡɭɛɚ ɞɨɥɛɹɤɚ; ɩɨɞɪɟɡ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ ɝɨɥɨɜɤɨɣ ɡɭɛɚ ɞɨɥɛɹɤɚ; ɢ ɨɛɪɚɡɨɜɚɧɢɟ ɛɨɥɶɲɨɣ ɩɟɪɟɯɨɞɧɨɣ ɤɪɢɜɨɣ ɜ ɨɫɧɨɜɚɧɢɢ ɡɭɛɚ ɤɨɥɟɫɚ, ɤɨɬɨɪɨɟ ɩɪɢɜɨɞɢɬ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɬɚɤɨɝɨ ɤɨɥɟɫɚ ɤ ɧɟɩɪɚɜɢɥɶɧɨɦɭ ɡɚɰɟɩɥɟɧɢɸ ɩɚɪɵ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ, ɱɬɨ ɩɪɨɹɜɥɹɟɬɫɹ ɡɧɚɱɢɬɟɥɶɧɵɦ ɲɭɦɨɦ ɩɪɢ ɪɚɛɨɬɟ. ɂɫɯɨɞɹ ɢɡ ɜɢɞɨɜ ɢɧɬɟɪɮɟɪɟɧɰɢɢ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ ɫ ɛɨɥɶɲɢɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ ɧɟɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɨɟɤɬɢɪɨɜɚɬɶ ɞɨɥɛɹɤ ɫ ɦɚɥɵɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ, ɬ.ɤ. ɷɬɨ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɫɪɟɡɚɧɢɸ ɩɪɨɮɢɥɹ ɭ ɜɟɪɲɢɧɵ ɡɭɛɶɟɜ ɤɨɥɟɫɚ. Ⱦɥɹ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɫ ɦɚɥɵɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ ɧɟɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɢɦɟɧɟɧɢɟ ɞɨɥɛɹɤɚ ɫ ɛɨɥɶɲɢɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ, ɬ.ɤ. ɷɬɨ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɩɨɞɪɟɡɚɧɢɸ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ, ɱɬɨ ɧɟɞɨɩɭɫɬɢɦɨ ɨɫɨɛɟɧɧɨ ɞɥɹ ɫɢɥɨɜɵɯ ɡɭɛɱɚɬɵɯ ɩɟɪɟɞɚɱ. ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɱɢɫɥɚ ɡɭɛɶɟɜ ɞɨɥɛɹɤɚ ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ ɜɨɡɦɨɠɧɨɫɬɶ ɲɥɢɮɨɜɚɧɢɹ ɡɭɛɶɟɜ ɧɚ ɡɭɛɨɲɥɢɮɨɜɚɥɶɧɨɦ ɫɬɚɧɤɟ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɷɬɨɣ ɨɩɟɪɚɰɢɢ ɩɪɢɦɟɧɹɟɬɫɹ ɞɜɚ ɜɢɞɚ ɨɛɨɪɭɞɨɜɚɧɢɹ: ɫ ɰɢɥɢɧɞɪɢɱɟɫɤɢɦ ɞɢɫɤɨɦ ɢ ɫɬɚɥɶɧɨɣ ɥɟɧɬɨɣ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɲɥɢɮɨɜɚɧɢɟ ɢɧɫɬɪɭɦɟɧɬɚ (ɞɨɥɛɹɤɚ ɢ ɲɟɜɟɪɚ) ɫ ɥɸɛɵɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ; ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɷɜɨɥɶɜɟɧɬɧɵɯ ɤɨɩɢɪɨɜ, ɤɨɬɨɪɵɟ ɩɨɡɜɨɥɹɸɬ ɩɪɨɢɡɜɟɫɬɢ ɲɥɢɮɨɜɚɧɢɟ ɡɭɛɶɟɜ ɢɧɫɬɪɭɦɟɧɬɚ ɫ ɱɢɫɥɨɦ ɡɭɛɶɟɜ ɜ ɨɩɪɟɞɟɥɟɧɧɨɦ ɞɢɚɩɚɡɨɧɟ. ȼ ɩɨɫɥɟɞɧɟɦ ɫɥɭɱɚɟ ɨɝɪɚɧɢɱɟ57

ɧɢɟ ɜ ɜɵɛɨɪɟ ɱɢɫɥɚ ɡɭɛɶɟɜ ɞɨɥɛɹɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɚɤɠɟ ɧɚɥɢɱɢɟɦ ɞɟɥɢɬɟɥɶɧɵɯ ɞɢɫɤɨɜ, ɤɨɬɨɪɵɟ ɩɨɫɬɚɜɥɹɸɬɫɹ ɫɨ ɫɬɚɧɤɨɦ. ȼ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɵɯ ɰɟɯɚɯ ɦɚɲɢɧɨɫɬɪɨɢɬɟɥɶɧɵɯ ɡɚɜɨɞɨɜ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɩɪɢɦɟɧɹɟɬɫɹ ɜɬɨɪɨɣ ɜɢɞ ɨɛɨɪɭɞɨɜɚɧɢɹ. ɂ ɷɬɨ ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɱɢɫɥɚ ɡɭɛɶɟɜ ɞɨɥɛɹɤɚ. ɉɪɢ ɪɚɫɱɟɬɟ ɱɢɫɥɚ ɡɭɛɶɟɜ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ ɬɚɤɠɟ ɧɚɥɢɱɢɟ ɤɨɩɢɪɨɜ ɧɚ ɡɭɛɨɞɨɥɛɟɠɧɨɦ ɫɬɚɧɤɟ, ɨɫɨɛɟɧɧɨ ɩɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɜ ɟɞɢɧɢɱɧɨɦ ɢ ɫɟɪɢɣɧɨɦ ɩɪɨɢɡɜɨɞɫɬɜɟ. ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ ɭɦɟɧɶɲɟɧɢɹ ɬɪɭɞɧɨɫɬɟɣ ɩɪɢ ɤɨɧɬɪɨɥɟ ɞɢɚɦɟɬɪɨɜ ɞɨɥɛɹɤɚ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɢɦɟɧɹɬɶ ɱɟɬɧɨɟ ɱɢɫɥɨ ɡɭɛɶɟɜ. ɉɨɫɥɟ ɜɵɛɨɪɚ ɱɢɫɥɚ ɡɭɛɶɟɜ ɞɨɥɛɹɤɚ ɪɚɫɱɟɬ ɫɜɨɞɢɬɫɹ ɤ ɨɩɪɟɞɟɥɟɧɢɸ ɢɫɯɨɞɧɵɯ ɪɚɫɫɬɨɹɧɢɣ (ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɢ ɨɬɪɢɰɚɬɟɥɶɧɨɝɨ), ɩɟɪɟɬɨɱɤɚ ɜ ɩɪɟɞɟɥɚɯ ɧɚɢɦɟɧɶɲɟɣ ɫɭɦɦɵ ɚɛɫɨɥɸɬɧɵɯ ɡɧɚɱɟɧɢɣ ɤɨɬɨɪɵɯ ɨɛɟɫɩɟɱɢɬ ɤɚɱɟɫɬɜɟɧɧɨɟ ɢɡɝɨɬɨɜɥɟɧɢɟ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ. Ⱦɥɹ ɩɪɹɦɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ ɢ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ, ɧɨ ɛɟɡ ɭɱɟɬɚ ɢɦɟɸɳɟɝɨɫɹ ɤɨɩɢɪɚ ɧɚ ɡɭɛɨɞɨɥɛɟɠɧɨɦ ɫɬɚɧɤɟ,

z ' = d '0 / m . t

(3.)

ɝɞɟ d'0 – ɧɨɦɢɧɚɥɶɧɵɣ ɞɢɚɦɟɬɪ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɞɨɥɛɹɤɚ, ɜɵɛɢɪɚɟɦɵɣ ɩɨ ɬɚɛɥ. 3. ɢɥɢ ɩɨ ɩɚɫɩɨɪɬɭ ɡɭɛɨɞɨɥɛɟɠɧɨɝɨ ɫɬɚɧɤɚ (ɤɚɬɚɥɨɠɧɨɦɭ ɥɢɫɬɤɭ). ɉɨɫɥɟ ɪɚɫɱɟɬɚ ɡɧɚɱɟɧɢɟ z' ɨɤɪɭɝɥɢɬɶ ɞɨ ɰɟɥɨɝɨ, ɥɭɱɲɟ ɱɟɬɧɨɝɨ ɱɢɫɥɚ ɢ ɩɟɪɟɫɱɢɬɚɬɶ ɡɧɚɱɟɧɢɟ ɧɨɦɢɧɚɥɶɧɨɝɨ ɞɢɚɦɟɬɪɚ d = z ⋅m . 0 0 t

(3.2)

Ⱦɥɹ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ ɫ ɭɱɟɬɨɦ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɤɨɩɢɪɚ ɧɚ ɡɭɛɨɞɨɥɛɟɠɧɨɦ ɫɬɚɧɤɟ

P ⋅ sin β z = z . 0 π ⋅m

(3.3)

ɝɞɟ Ɋz – ɲɚɝ ɜɢɧɬɨɜɨɝɨ ɤɨɩɢɪɚ. Ɋz = 96 ɢ 75,96 ɦɦ. ȼ ɫɥɭɱɚɟ ɡɚɞɚɧɢɹ ɜ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɦɨɞɟɥɢ ɡɭɛɨɞɨɥɛɟɠɧɨɝɨ ɫɬɚɧɤɚ ɦɨɝɭɬ ɢɦɟɬɶ ɦɟɫɬɨ ɤɨɩɢɪɵ ɫ ɞɪɭɝɢɦɢ ɡɧɚɱɟɧɢɹɦɢ Ɋz. 58

Ɍɚɛɥɢɰɚ 3.. Ɍɢɩ ɞɨɥɛɹɤɚ

ɉɪɹɦɨɡɭɛɵɟ ɞɢɫɤɨɜɵɣ ɢ ɱɚɲɟɱɧɵɣ

ɉɪɹɦɨɡɭɛɵɟ ɞɢɫɤɨɜɵɣ ɢ ɱɚɲɟɱɧɵɣ ɑɚɲɟɱɧɵɣ ɩɪɹɦɨɡɭɛɵɣ Ʉɨɫɨɡɭɛɵɣ ɞɢɫɤɨɜɵɣ

ɇɨɪɦɚɥɶɧɵɣ ɦɨɞɭɥɶ m, ɦɦ –,5 ,75–2,5 2,75–5 –,75 2–5 5,5–8 2–3,5 3,75–4 5–0 6–7 8–0 8–2 –,5 ,75–2,75 3–3,5 –,5 ,75–4 4,5–6

ȼɵɫɨɬɚ ɞɨɥɛɹɤɚ ɇɨɦɢɧɚɥɶɧɵɣ ɞɢɚɦɟɬɪ ɇɨɜɨɝɨ ɂɡɧɨɲɟɧ- Ɋɚɛɨɱɟɣ d'0, ɦɦ ȼ ɧɨɝɨ ȼɢɡɧ ɱɚɫɬɢ ȼp 80 2 4 8 80 5 5 0 80 7 7 0 00 7 9–6 8– 00 20 7–8 3– 00 22 8–7 4–5 25 22 7 5 25 24 8 6 25 28 9 7 50 30 9,5 20,5 60 32 2 20 200 50 50 50 00 00 00

40 2 5 7 7 20 22

3,5 4 5 6 8 9 8

26,5 8 0 9 2 4

ɉɨɫɥɟ ɪɚɫɱɺɬɚ z0 ɨɤɪɭɝɥɢɬɶ ɞɨ ɰɟɥɨɝɨ, ɥɭɱɲɟ ɱɺɬɧɨɝɨ ɱɢɫɥɚ. ɑɢɫɥɨ z0 ɤɚɤ ɞɥɹ ɩɪɹɦɨɡɭɛɨɝɨ, ɬɚɤ ɢ ɞɥɹ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ ɞɨɥɠɧɨ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɱɢɫɥɭ ɡɭɛɶɟɜ (ɜɩɚɞɢɧ) ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɞɢɫɤɟ ɡɭɛɨɲɥɢɮɨɜɚɥɶɧɨɝɨ ɫɬɚɧɤɚ: 7, 8, 20, 2, 22, 23, 24, 25, 27, 28, 29, 30, 3, 32, 34, 36, 37, 38, 40, 4, 42, 43, 44, 45, 46, 47, 48, 5, 52, 53, 54, 56, 58, 60, 6, 62, 63, 64, 66, 67, 68, 70, 72, 73, 74, 75, 76, 78, 80, 82, 83, 88, 90, 00, 02, 03, 5. Ⱦɥɹ ɩɪɢɧɹɬɨɝɨ ɱɢɫɥɚ ɡɭɛɶɟɜ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ ɩɟɪɟɫɱɢɬɚɬɶ ɡɧɚɱɟɧɢɟ ɭɝɥɚ ȕ: β = arcsin

π ⋅m⋅ z P z

(3.4)

0.

ɉɨ ɫɨɝɥɚɫɨɜɚɧɢɸ ɫ ɤɨɧɫɬɪɭɤɬɨɪɨɦ ɡɭɛɱɚɬɨɣ ɩɟɪɟɞɚɱɢ ɞɨɩɭɫɤɚɟɬɫɹ ɢɡɦɟɧɟɧɢɟ ɭɝɥɚ ȕ ɜ ɩɪɟɞɟɥɚɯ ± 3˚ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɡɚɞɚɧɧɵɦ ɡɧɚɱɟɧɢɟɦ.

59

ɉɟɪɟɫɱɢɬɚɬɶ ɡɧɚɱɟɧɢɟ ɧɨɦɢɧɚɥɶɧɨɝɨ ɞɢɚɦɟɬɪɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ m⋅z 0. d = 0 cos β

(3.5)

Ⱦɢɚɦɟɬɪ ɨɫɧɨɜɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɞɨɥɛɹɤɚ ɢ ɬɨɪɰɨɜɵɣ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ: d

⎛ tgα ⎞ ⎟⎟; = d ⋅ cos⎜⎜ arctg b 0 β cos ⎝ ⎠ 0

tgα . α = arctg t cos β

(3.6)

ɉɪɢ ɭɫɥɨɜɢɢ ɲɥɢɮɨɜɚɧɢɹ ɡɭɛɶɟɜ ɞɨɥɛɹɤɚ ɧɚ ɫɬɚɧɤɟ ɫ ɧɚɛɨɪɨɦ ɷɜɨɥɶɜɟɧɬɧɵɯ ɤɨɩɢɪɨɜ ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ ɜɨɡɦɨɠɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɦɟɸɳɢɯɫɹ ɤɨɩɢɪɨɜ. Ⱦɢɚɦɟɬɪ ɨɫɧɨɜɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɩɢɪɚ Dɤ ɞɨɥɠɟɧ ɛɵɬɶ ɬɨɱɧɨ ɢɥɢ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɪɚɜɟɧ d0: Dɤ = d0 ɢɥɢ Dɤ § d0 .

(3.7)

Ʉɪɨɦɟ ɬɨɝɨ, Dɤ ɞɨɥɠɟɧ ɛɵɬɶ ɪɚɜɟɧ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɡɧɚɱɟɧɢɣ: 8; 2; 5; 25,4; 26; 38,; 50,8; 55; 62; 63,5; 72; 75; 76,2; 77; 88,9; 99; 00; 0,6; 03; 97; 25; 42; 50; 62; 64; 7; 78; 80; 98; 202; 225 ɦɦ. ɍɝɨɥ ɭɫɬɚɧɨɜɤɢ ɫɚɥɚɡɨɤ ɡɭɛɨɲɥɢɮɨɜɚɥɶɧɨɝɨ ɫɬɚɧɤɚ d

α

ɭɫɬ

= arccos

b 0. D ɤ

(3.8)

Ⱦɥɹ ɪɚɜɧɨɦɟɪɧɨɝɨ ɢɡɧɨɫɚ ɲɥɢɮɨɜɚɥɶɧɨɝɨ ɤɪɭɝɚ ɧɟɨɛɯɨɞɢɦɨ ɜɵɞɟɪɠɚɬɶ ɭɫɥɨɜɢɟ > (α − 6°). (α + °) ≥ α t ɭɫɬ t

(3.9)

ȿɫɥɢ ɷɬɨ ɭɫɥɨɜɢɟ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɫɥɟɞɭɟɬ ɩɪɨɢɡɜɟɫɬɢ ɩɟɪɟɪɚɫɱɟɬ ɜɟɥɢɱɢɧɵ Įɭɫɬ ɫ ɧɨɜɵɦ ɡɧɚɱɟɧɢɟɦ ɱɢɫɥɚ ɡɭɛɶɟɜ z0, ɜɡɹɬɨɦ ɢɡ ɪɹɞɚ ɱɢɫɟɥ ɡɭɛɶɟɜ ɞɟɥɢɬɟɥɶɧɨɝɨ ɞɢɫɤɚ ɡɭɛɨɲɥɢɮɨɜɚɥɶɧɨɝɨ ɫɬɚɧɤɚ, ɩɪɢɱɟɦ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɧɢɦɚɬɶ ɞɜɚ ɦɟɧɶɲɢɯ ɢ ɞɜɚ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɟɪɜɵɦ ɩɪɢɧɹ-

60

ɬɵɦ ɡɧɚɱɟɧɢɟɦ z0. Ɋɚɫɱɟɬ ɩɨɜɬɨɪɢɬɶ ɩɨ ɮɨɪɦɭɥɚɦ (3.4–3.8) ɡɚɧɨɜɨ. ɉɪɨɜɟɪɢɬɶ ɭɫɥɨɜɢɟ (3.9). ȿɫɥɢ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɜ ɞɚɥɶɧɟɣɲɢɯ ɪɚɫɱɟɬɚɯ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɪɢɧɹɬɨɟ ɡɧɚɱɟɧɢɟ z0. ȿɫɥɢ ɩɨɫɥɟ ɜɫɟɯ ɩɨɩɵɬɨɤ ɧɟ ɭɞɚɥɨɫɶ ɭɫɬɚɧɨɜɢɬɶ ɡɧɚɱɟɧɢɹ z0, ɨɬɜɟɱɚɸɳɟɟ ɬɪɟɛɨɜɚɧɢɸ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ Ɋz ɢ ɢɡɦɟɧɟɧɢɹ ȕ ɜ ɩɪɟɞɟɥɚɯ ±3˚ ɢ Įɭɫɬ, ɬɨ ɩɪɢɧɢɦɚɟɬɫɹ ɩɟɪɜɨɟ ɡɧɚɱɟɧɢɟ z0. Ɍɨɝɞɚ ɞɥɹ ɲɥɢɮɨɜɚɧɢɹ ɡɭɛɶɟɜ ɞɨɥɛɹɤɚ ɩɪɢɞɟɬɫɹ ɢɡɝɨɬɨɜɢɬɶ ɧɨɜɵɣ ɤɨɩɢɪ ɫ ɞɪɭɝɢɦɢ ɡɧɚɱɟɧɢɹɦɢ Ɋz ɢɥɢ ɩɪɟɞɭɫɦɨɬɪɟɬɶ ɲɥɢɮɨɜɚɧɢɟ ɡɭɛɶɟɜ ɧɚ ɫɬɚɧɤɚɯ, ɤɨɬɨɪɵɟ ɩɨɡɜɨɥɹɸɬ ɲɥɢɮɨɜɚɧɢɟ ɢɧɫɬɪɭɦɟɧɬɚ ɫ ɥɸɛɵɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ. ȼ ɫɥɭɱɚɟ, ɟɫɥɢ ɢɡɦɟɧɢɥɨɫɶ ɡɧɚɱɟɧɢɟ ɭɝɥɚ ȕ, ɬɨ ɩɨ ɮɨɪɦɭɥɚɦ ɪɚɡɞɟɥɚ ɩɪɨɢɡɜɟɫɬɢ ɩɟɪɟɪɚɫɱɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ. Ⱦɥɹ ɫɥɭɱɚɹ ɪɚɫɱɟɬɚ z0 ɧɚ ɢɧɠɟɧɟɪɧɨɦ ɦɢɤɪɨɤɚɥɶɤɭɥɹɬɨɪɟ ɧɢɠɟ ɩɪɢɜɟɞɟɧ ɩɪɢɦɟɪ ɪɚɫɱɟɬɚ ɩɚɪɚɦɟɬɪɨɜ z0 , d0 , Dɤ ɞɥɹ ɞɨɥɛɹɤɚ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɨɝɨ ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɤɨɫɨɡɭɛɨɝɨ ɤɨɥɟɫɚ ɩɪɚɜɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɫ m = 3 ɦɦ; Į = 20˚; ȕ = 22˚; z1 = 25˚; h*a = ; x1 = 0, ɧɚɯɨɞɹɳɟɝɨɫɹ ɜ ɡɚɰɟɩɥɟɧɢɢ ɫ ɤɨɥɟɫɨɦ z2 = 75; x2=0. ɋɬɟɩɟɧɶ ɬɨɱɧɨɫɬɢ ɡɭɛɱɚɬɨɣ ɩɚɪɵ ɩɨ ɧɨɪɦɚɦ ɬɨɱɧɨɫɬɢ ɢ ɜɜɢɞɭ ɫɨɩɪɹɠɟɧɢɹ 7–ɋ ɩɨ ȽɈɋɌ 643-8. P ⋅ sin β 96 ⋅ sin 22 ° = = 47 ,6; z' = z 0 π ⋅m π ⋅3 P ⋅ sin β 75,96 ⋅ sin 22° z' = z = = 29,9. 0 π ⋅m π ⋅3

ɉɪɢɧɢɦɚɟɦ zǯ0 = 48; zǯ0 = 30. ɍɱɢɬɵɜɚɹ ɦɟɧɶɲɭɸ ɫɬɨɢɦɨɫɬɶ ɞɨɥɛɹɤɚ ɩɪɢ ɦɟɧɶɲɟɦ ɱɢɫɥɟ ɡɭɛɶɟɜ (ɬɨɱɧɨ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢɫɯɨɞɹ ɢɡ ɦɢɧɢɦɭɦɚ ɡɚɬɪɚɬ ɧɚ ɢɧɫɬɪɭɦɟɧɬ ɩɪɢ ɢɡɝɨɬɨɜɥɟɧɢɢ ɨɞɧɨɝɨ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ) ɢ ɫɨɨɛɪɚɡɭɹɫɶ ɫ ɞɚɧɧɵɦɢ ɬɚɛɥ. 3., ɫɥɟɞɭɟɬ ɩɪɢɧɹɬɶ zǯ0 = 30, ɩɪɢ ɷɬɨɦ: π ⋅ m ⋅ z0 π ⋅ 3 ⋅ 30 β = arcsin = arcsin = 22,08655° Pz 75,96 m ⋅ z0 3 ⋅ 30 = = 97,27604; d0 = cos β cos 22,08655 6

(ɬ.ɟ. ɦɟɧɶɲɟ 25˚);

tgα tg 20° d b = d 0 ⋅cos( arctg ) = 97 ,27604 ⋅cos( arctg ) = 90 , 403 . ° β cos cos 22 , 08655 0

ȿɫɥɢ ɭɱɟɫɬɶ, ɱɬɨ ɞɨɥɠɧɨ ɛɵɬɶ Dɤ = d0 ɢɥɢ Dɤ § d0, ɬɨ ɢɡ ɪɹɞɚ Dɤ ɫɥɟɞɭɟɬ ɩɪɢɧɹɬɶ Dɤ =00 ɦɦ. Ɍɨɝɞɚ

⎛d ⎜ b = arccos⎜ 0 α ɭɫɬ ⎜ Dɤ ⎝

⎞ ⎟ ⎟ = arccos(90,403 / 00) = 25,30704°. ⎟ ⎠

ɉɪɢ ɷɬɨɦ ɭɫɥɨɜɢɟ ≥ (α − 6°), (α + °) ≥ α t ɭɫɬ t

(2,4° + °) ≥ α

ɭɫɬ

≥ (2,4° − 6°),

22,4° > α ɭɫɬ > 5,4° ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ. ɂɡ ɪɹɞɚ ɱɢɫɟɥ ɡɭɛɶɟɜ ɞɟɥɢɬɟɥɶɧɨɝɨ ɞɢɫɤɚ ɡɭɛɨɲɥɢɮɨɜɚɥɶɧɨɝɨ ɫɬɚɧɤɚ ɦɨɠɧɨ ɜɵɛɪɚɬɶ z0 = 29; 28; 3; 32. Ɋɚɫɱɟɬɵ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɩɪɢ z0 = 29 ɢ Dɤ = 90 ɩɨɫɥɟɞɧɟɟ ɭɫɥɨɜɢɟ ɬɚɤɠɟ ɧɟ ɜɵɞɟɪɠɢɜɚɟɬɫɹ. ɍɫɥɨɜɢɟ ɜɵɞɟɪɠɢɜɚɟɬɫɹ ɩɪɢ z0 = 29 ɢ Dɤ = 88,9 ɦɦ. (22,2˚ > 9,8˚ > 5,2˚) ɢ ɩɪɢ z0 = 3 ɢ Dɤ = 00 ɦɦ (22,5˚ > 20,5˚ > 5,5˚). ɉɪɢɱɟɦ ɩɪɢ z0 = 28 ɭɝɨɥ ȕ = 20,5448˚ ɢ ɩɪɢ z0 = 3 ɭɝɨɥ ȕ = 22,8638˚. Ɍɚɤɢɟ ɡɧɚɱɟɧɢɹ ɭɝɥɨɜ ɜɩɨɥɧɟ ɞɨɩɭɫɬɢɦɵ, ɬ.ɤ. ɩɨɥɭɱɢɥɢɫɶ ɨɬɤɥɨɧɟɧɢɹ ɨɬ ɡɚɞɚɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ –,5˚ ɢ +0,6˚, ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜɵɞɟɪɠɚɧɨ ɭɫɥɨɜɢɟ ɢɡɦɟɧɟɧɢɹ ɜ ɩɪɟɞɟɥɚɯ ±3˚. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɨɠɧɨ ɩɪɢɧɹɬɶ z0 = 28 ɢ z0 = 3. ɂɡ ɷɬɢɯ ɞɜɭɯ ɡɧɚɱɟɧɢɣ ɩɟɪɜɨɟ ɡɧɚɱɟɧɢɟ ɨɛɟɫɩɟɱɢɬ ɦɟɧɶɲɭɸ ɫɬɨɢɦɨɫɬɶ ɞɨɥɛɹɤɚ, ɜɬɨɪɨɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɦɟɧɶɲɟɦɭ ɨɬɤɥɨɧɟɧɢɸ ɩɨ ɭɝɥɭ ȕ, ɬ.ɟ. ɦɟɧɶɲɟɦɭ ɢɡɦɟɧɟɧɢɸ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ, ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɚɢɦɟɧɶɲɟɦɭ ɢɡɦɟɧɟɧɢɸ ɭɫɥɨɜɢɣ ɪɚɛɨɬɵ ɡɭɛɱɚɬɨɣ ɩɟɪɟɞɚɱɢ.

62

ɉɨɫɥɟ ɩɪɢɧɹɬɨɝɨ ɡɧɚɱɟɧɢɹ z0 ɫɥɟɞɭɟɬ ɩɟɪɟɫɱɢɬɚɬɶ ɡɧɚɱɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɩɨ ɮɨɪɦɭɥɚɦ ɪɚɡɞɟɥɚ . Ɋɚɫɱɟɬ ɢɫɯɨɞɧɵɯ ɪɚɫɫɬɨɹɧɢɣ ɧɚɱɢɧɚɟɬɫɹ ɫ ɨɩɪɟɞɟɥɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɞɨɥɛɹɤɚ ɜ ɢɫɯɨɞɧɨɦ ɫɟɱɟɧɢɢ. Ⱦɢɚɦɟɬɪ ɧɚɪɭɠɧɵɣ ɨɤɪɭɠɧɨɫɬɢ ɜ ɢɫɯɨɞɧɨɦ ɫɟɱɟɧɢɢ d'

a

= d +d −d . f 0 0

(3.0)

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɧɨɪɦɚɥɢ ɜ ɢɫɯɨɞɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ S'

n

=π ⋅m− S 0

n

.

(3.)

Ɍɨɪɰɨɜɵɣ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɧɚ ɨɤɪɭɠɧɨɫɬɢ ɜɟɪɲɢɧ d

α'

at

= arccos 0

b 0 . ' α a 0

(3.2)

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɧɚ ɜɟɪɲɢɧɟ ɜ ɢɫɯɨɞɧɨɦ ɫɟɱɟɧɢɢ ɩɨ ɬɨɪɰɭ ⎛ S 'n0 ⎞ + invα t − invα 'at 0 ⎟⎟ S 'at 0 = d 'a 0 ⋅⎜⎜ ⎝ d 0 ⋅ cos β ⎠

(3.3)

Ɉɩɪɟɞɟɥɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɤɨɪɪɟɤɰɢɢ ɢ ɢɫɯɨɞɧɵɯ ɪɚɫɫɬɨɹɧɢɣ Ɇɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɚɹ ɬɨɥɳɢɧɚ ɡɭɛɚ ɩɪɢ ɜɟɪɲɢɧɟ ɭ ɧɨɜɨɝɨ ɞɨɥɛɹɤɚ: ɩɪɢ 80 > d0 > 50 ɩɪɢ d0 > 80

S

at

S

= 0 min

at

=

0,2595m − 0,0375 ; cos β

0,8m − 0,72 . cos β

(3.4)

0 min ɉɟɪɟɞɧɢɣ ɭɝɨɥ Ȗɜ ɞɨɥɛɹɤɚ ɢ ɡɚɞɧɢɣ ɭɝɨɥ ɩɪɢ ɜɟɪɲɢɧɟ Įɜ ɰɟɥɟɫɨɨɛɪɚɡɧɨ

ɩɪɢɧɹɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ȽɈɋɌ 9323-79 []: γ = 5°;

(3.5) α = 6°. ɜ ɋɥɟɞɭɟɬ ɩɪɨɜɟɪɢɬɶ ɞɨɫɬɚɬɨɱɧɨɫɬɶ ɡɚɞɧɟɝɨ ɭɝɥɚ ɜ ɧɨɪɦɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ (ɜ ɩɥɨɫɤɨɫɬɢ, ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɨɫɧɨɜɧɨɦɭ ɰɢɥɢɧɞɪɭ) ɩɨ ɮɨɪɦɭɥɟ:

α = arctg (tgα ⋅ sin α ). n ɜ 63

(3.6) Ⱦɨɥɠɧɨ ɛɵɬɶ Įn 2˚30'. ȿɫɥɢ ɷɬɨ ɭɫɥɨɜɢɟ ɧɟ ɜɵɞɟɪɠɢɜɚɟɬɫɹ, ɬɨ ɩɪɢɧɢɦɚɸɬ Įn = 2˚30' – 3˚ ɢ ɩɨ ɮɨɪɦɭɥɟ tgα n. α = arctg ɜ sin α ɨɩɪɟɞɟɥɹɸɬ ɧɟɨɛɯɨɞɢɦɨɟ ɡɧɚɱɟɧɢɟ ɭɝɥɚ Įɜ.

(3.7)

ɇɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɞɨɥɛɹɤɚ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɫɦɟɳɟɧɢɹ x'0,

d ' ' a 0 = d ' a 0 + 2 x '0 ⋅m

*

,

(3.8)

ɝɞɟ x'0 – ɤɨɷɮɮɢɰɢɟɧɬ ɫɦɟɳɟɧɢɹ ɢɫɯɨɞɧɨɝɨ ɤɨɧɬɭɪɚ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɨɣ ɬɨɥɳɢɧɟ ɡɭɛɚ ɩɪɢ ɜɟɪɲɢɧɟ ɞɨɥɛɹɤɚ. Ɍɨɪɰɨɜɵɣ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɧɚ ɨɤɪɭɠɧɨɫɬɢ ɜɟɪɲɢɧ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɤɨɷɮɮɢɰɢɟɧɬɭ x'0, ⎛ d ⎜ ɜ 0 α'' = arccos⎜ at d ' ' ⎜⎜ a 0 0 ⎝

⎞ ⎟ ⎟. ⎟⎟ ⎠

(3.9)

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɧɚ ɜɟɪɲɢɧɟ ɜ ɫɟɱɟɧɢɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɤɨɷɮɮɢɰɢɟɧɬɭ x'0, ⎡ S 'n +2 x'0 ⋅m ⋅ tgα ⎢ S '' + (tgα − α ) − (tgα' ' −α ' ' = d ' ' ⋅⎢ 0 at a t t at at d ⋅ cos β 0 0 ⎢ 0 0 0 ⎣

⎤ ⎥ )⎥. ⎥⎦

(3.20)

ɉɪɢɪɚɜɧɹɜ S''at0 = Sat0, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ x'0. Ɍɚɤ ɤɚɤ ɭɪɚɜɧɟɧɢɟ ⎡ S 'n +2 x'0 ⋅m ⋅ tgα ⎢ S = d ' ' ⋅⎢ 0 + (tgα − α ) − (tgα' ' −α ' ' at a t t at at ⋅ β d cos 0 min 0 ⎢ 0 0 0 ⎣

⎤ ⎥ )⎥. ⎥⎦

(3.2)

ɬɪɚɧɫɰɟɧɞɟɧɬɧɨɟ, ɬɨ ɪɟɲɢɬɶ ɟɝɨ ɹɜɧɵɦ ɩɭɬɟɦ ɧɟ ɭɞɚɟɬɫɹ. ɇɚ ɗȼɆ ɨɧɨ ɪɟɲɚɟɬɫɹ ɦɟɬɨɞɨɦ ɢɬɟɪɚɰɢɢ.

______________________ * Ɏɨɪɦɭɥɵ 3.8–3.23 ɨɬɧɨɫɹɬɫɹ ɬɨɥɶɤɨ ɪɚɫɱɟɬɭ ɞɨɥɛɹɤɚ ɧɚ ɗȼɆ 64

ɂɡɦɟɧɟɧɢɟ x'0 ɡɚɞɚɟɬɫɹ ɜ ɩɪɟɞɟɥɚɯ ±2. ɉɨɞɫɬɚɜɢɜ ɬɟɤɭɳɟɟ ɡɧɚɱɟɧɢɟ x'0 ɜ ɮɨɪɦɭɥɵ 3.8–3.20 ɢ ɫɪɚɜɧɢɜɚɹ ɡɧɚɱɟɧɢɟ S''at0 ɫɨ ɡɧɚɱɟɧɢɟɦ Sat0, ɩɨɞɫɱɢɬɚɧɧɵɦ ɩɨ ɮɨɪɦɭɥɚɦ 3.2, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ x'0 ɩɪɢ ɬɨɱɧɨɫɬɢ ɪɟɲɟɧɢɹ (S ' '

at

−S 0

at

(3.22)

) ≤ 0,0ɦɦ. 0 min

ɂɫɯɨɞɧɨɟ ɪɚɫɫɬɨɹɧɢɟ, ɥɢɦɢɬɢɪɭɟɦɨɟ ɡɚɨɫɬɪɟɧɢɟɦ ɡɭɛɚ ɞɨɥɛɹɤɚ, a'

x ⋅m = 0 ⋅ cos β . H tgα ɜ

(3.23)

ɉɪɢ ɪɭɱɧɨɦ ɪɚɫɱɟɬɟ ɢɫɯɨɞɧɨɟ ɪɚɫɫɬɨɹɧɢɟ, ɥɢɦɢɬɢɪɭɟɦɨɟ ɡɚɨɫɬɪɟɧɢɟɦ ɡɭɛɚ ɞɨɥɛɹɤɚ, ɩɪɢɛɥɢɠɟɧɧɨ ɦɨɠɧɨ ɩɨɞɫɱɢɬɚɬɶ ɩɨ ɦɟɬɨɞɢɤɟ, ɩɪɟɞɥɨɠɟɧɧɨɣ ȼ.Ɏ. Ɋɨɦɚɧɨɜɵɦ [0]: S ⎛ at ⎜ 0 min ⎜ S 'at − cos β ⎜ 0 ⎝

a′ = H

⎞ ⎟ ⎟ ⋅ d 'a ⎟ 0 ⎠ (d '

2( d '

a

⋅tgα' 0

at

−S ' 0

) ⋅ tgα − at ɜ 0

a

)2 ⋅ C 0 d

(3.24)

,

0

ɝɞɟ ɋ – ɜɫɩɨɦɨɝɚɬɟɥɶɧɚɹ ɜɟɥɢɱɢɧɚ, ɨɩɪɟɞɟɥɹɟɦɚɹ ɩɨ ɮɨɪɦɭɥɟ: ⎛ tgα ⋅ tgα ɜ C = tg ⎜ β + arctg ⎜ − tgγ ⋅ tgα ɜ ⎝

ɉɪɢ ȕ = 0˚

⎞ ⎛ tgα ⋅ tgα ɜ ⎟ − tg ⎜ β − arctg ⎟ ⎜ − tgγ ⋅ tgα ɜ ⎠ ⎝

⎛ tgα ⋅ tgα ⎞ ⎟. ɜ C = 2tg ⎜ arctg ⎜ − tgγ ⋅ tgα ⎟ ɜ⎠ ⎝

⎞ ⎟. ⎟ ⎠

(3.25)

ɋɬɚɧɨɱɧɵɣ ɭɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɧɨɜɨɝɨ ɞɨɥɛɹɤɚ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɨɛɪɚɛɨɬɤɭ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ, ) ⋅ ( d − 2 ρ ⋅ sin α ) b f p t 0 α ' ' = arccos . tw 2 2 2 2 − 4ρ (d + d ) + d − d b b f b p 0 0 2(d

b

+d

65

(3.26)

ɉɨɥɨɠɢɬɟɥɶɧɨɟ ɢɫɯɨɞɧɨɟ ɪɚɫɫɬɨɹɧɢɟ, ɨɩɪɟɞɟɥɹɸɳɟɟ ɩɨɥɧɭɸ ɨɛɪɚɛɨɬɤɭ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ, α''

H

=

(invα ' '

tw

−invα ) ⋅ ( d + d ) − 2 x ⋅ tgα ⋅ m t t 0 . C

(3.27)

ɉɪɢɧɢɦɚɟɬɫɹ ɜɟɥɢɱɢɧɚ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɢɫɯɨɞɧɨɝɨ ɪɚɫɫɬɨɹɧɢɹ ɚɇ. ɚɇ – ɷɬɨ ɧɚɢɦɟɧɶɲɚɹ ɢɡ ɜɟɥɢɱɢɧ ɚ'ɇ ɢ ɚ''ɇ, ɬ.ɟ. ɟɫɥɢ ɚ'ɇ - ɚ''ɇ > 0, ɬɨ ɚɇ = ɚ''ɇ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɚɇ = ɚ'ɇ. ɋɬɚɧɨɱɧɵɣ ɭɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɩɟɪɟɬɨɱɟɧɧɨɝɨ ɞɨɥɛɹɤɚ, ɝɚɪɚɧɬɢɪɭɸɳɢɣ ɨɬɫɭɬɫɬɜɢɟ ɫɪɟɡɚɧɢɹ ɢɥɢ ɧɟɩɨɥɧɨɣ ɨɛɪɚɛɨɬɤɢ ɩɪɨɮɢɥɹ ɭ ɜɟɪɲɢɧɵ ɡɭɛɶɟɜ ɤɨɥɟɫɚ (ɩɨɹɜɥɹɟɬɫɹ ɜɫɥɟɞɫɬɜɢɟ ɪɚɛɨɬɵ ɧɟɷɜɨɥɶɜɟɧɬɧɨɣ ɭ ɨɫɧɨɜɚɧɢɹ ɱɚɫɬɶɸ ɩɪɨɮɢɥɹ ɡɭɛɚ ɞɨɥɛɹɤɚ),

α′tw′ = arctg

2(ρ a + ρ0 ) . db + d b0

(3.28)

ɝɞɟ ȡ10 – ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɩɪɨɮɢɥɹ ɡɭɛɚ ɞɨɥɛɹɤɚ, ɩɪɢɧɢɦɚɟɦɵɣ ɪɚɜɧɵɦ: ȡ10 = 3 ɦɦ ɩɪɢ d0 = 80 ɦɦ; ȡ10 = 5 ɦɦ ɩɪɢ d0 = 00÷200 ɦɦ; ȡ10 = 2 ɦɦ ɩɪɢ d0 50 ɦɦ. ȿɫɥɢ df1 < db1, ɬɨ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫɬɚɧɨɱɧɵɣ ɭɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɩɟɪɟɬɨɱɟɧɧɨɝɨ ɞɨɥɛɹɤɚ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɧɚɱɚɥɨ ɩɨɞɪɟɡɤɢ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ, ɩɨ ɮɨɪɦɭɥɟ ⋅ (d + d ) f b b 0 . 2 2 (d + d ) + d − d 2 b b f b 0 0 2d

α IV = arccos tw

(3.29)

ɉɪɢɧɢɦɚɟɬɫɹ ɫɬɚɧɨɱɧɵɣ ɭɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɩɟɪɟɬɨɱɟɧɧɨɝɨ ɞɨɥɛɹɤɚ Įtwc. ȿɫɥɢ df1 < db1, ɬɨ Įtwc – ɧɚɢɛɨɥɶɲɢɣ ɢɡ ɭɝɥɨɜ ĮIIItw ɢ ĮIVtw, ɬ.ɟ. ɟɫɥɢ ĮIIItw - ĮIVtw > 0, ɬɨ Įtwc = ĮIIItw. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ Įtwc = ĮIVtw. Ɉɬɪɢɰɚɬɟɥɶɧɨɟ ɢɫɯɨɞɧɨɟ ɪɚɫɫɬɨɹɧɢɟ a

C

=

(invα

twc

− invα ) ⋅ (d + d ) − 2 x ⋅ tgα ⋅ m t ɜ 0 . C

(3.30)

Ɇɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɚɹ ɜɟɥɢɱɢɧɚ ɫɬɚɱɢɜɚɧɢɹ H = aH – aC.

(3.3)

66

Ɉɩɪɟɞɟɥɟɧɢɟ ɜɟɥɢɱɢɧɵ ɢɫɯɨɞɧɨɝɨ ɪɚɫɫɬɨɹɧɢɹ Ⱥ: – ɟɫɥɢ ɇ ȼɪ, ɬɨ ɩɪɢɧɢɦɚɟɬɫɹ ȼɪ = ɇ, Ⱥ = ɚɇ; – ɟɫɥɢ ɇ > ȼɪ, ɬɨ: ɚ) ɩɪɢ ɚɇ < 0,5ȼɪ, ɜɟɥɢɱɢɧɚ Ⱥ = ɚɇ; ɛ) ɩɪɢ

ɚɇ > 0,5ȼɪ | ɚɋ | > 0,5ȼɪ – Ⱥ = 0,5ȼɪ;

ɜ) ɩɪɢ | ɚɋ | < 0,5ȼɪ

– Ⱥ = ȼɪ - | ɚɋ |.

ȼɪ – ɜɵɫɨɬɚ ɪɚɛɨɱɟɣ ɱɚɫɬɢ (ɫɦ. ɬɚɛɥ. 3.). ȼɟɥɢɱɢɧɭ Ⱥ ɨɤɪɭɝɥɢɬɶ ɫ ɬɨɱɧɨɫɬɶɸ ɨɞɧɨɝɨ ɡɧɚɤɚ ɩɨɫɥɟ ɡɚɩɹɬɨɣ. 3.2. Ɉɩɪɟɞɟɥɟɧɢɟ ɱɟɪɬɟɠɧɵɯ ɪɚɡɦɟɪɨɜ ɞɨɥɛɹɤɚ ɋɬɚɧɨɱɧɵɣ ɭɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɩɨ ɬɨɪɰɭ ɧɨɜɨɝɨ ɞɨɥɛɹɤɚ ɢ ɤɨɥɟɫɚ invα

= invα + twH t

2 tgα ⋅ ( x + x ) 0 , ɝɞɟ x = A ⋅ tgα ɜ . 0 m ⋅ cos β z +z 0

(3.32)

ɍɝɨɥ ĮtwH ɩɨ inv ĮtwH ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɦɟɬɨɞɨɦ ɢɬɟɪɚɰɢɢ ɧɚ ɗȼɆ. ɋɬɚɧɨɱɧɵɣ ɭɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɩɨ ɬɨɪɰɭ ɫɬɚɧɨɱɧɨɝɨ ɞɨɥɛɹɤɚ ɢ ɤɨɥɟɫɚ

invα

ɝɞɟ

twC

ɮɚɤɬ

= invα + t

2tgα ⋅ ( x + x ) 0C . z +z 0

(3.33)

( A − B' ) ⋅ tgα p ɜ = x . 0C m ⋅ cos β

ȼ ′P – ɩɪɢɧɹɬɚɹ ɜɟɥɢɱɢɧɚ ɫɬɚɱɢɜɚɧɢɹ:

ɟɫɥɢ ɇ ȼɪ, ɬɨ ȼ'ɪ = ȼɪ;

(3.34)

ɟɫɥɢ ɇ < ȼɪ, ɬɨ ȼ'ɪ = ɇ. ȼɵɫɨɬɚ ɞɨɥɛɹɤɚ B = H + Bɢɡɧ, ɟɫɥɢ H ȼɪ; B = ȼ'ɪ + Bɢɡɧ, ɟɫɥɢ H > ȼɪ. Bɢɡɧ – ɜɵɫɨɬɚ ɢɡɧɨɲɟɧɧɨɝɨ ɞɨɥɛɹɤɚ, ɩɪɢɜɟɞɟɧɚ ɜ ɬɚɛɥ. 3..

67

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɩɨ ɧɨɪɦɚɥɢ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɡɭɛɚ

= S ' + A ⋅ c ⋅ cos β . n n 0 0 ɇɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɧɨɜɨɝɨ ɞɨɥɛɹɤɚ S

(3.35)

+d b b 0 −d . d = a f cos α 0 twH d

(3.36)

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɜɟɪɯɭ ɞɨɥɛɹɤɚ ⎛ S n ⎜ 0 + invα − invα = d ⋅⎜ S t at an a 0 0 ⎜ d 0 ⋅ cos β 0 ⎝

⎛ d 0 ⋅ cos α t ⎜ d a0 ⎝

ɝɞɟ α at0 = arccos⎜

⎞ ⎛ d ⋅ tgβ ⎞ ⎟ a0 ⎜ ⎟; ⎟ ⋅ cos⎜ arctg ⎟ d ⎟ 0 ⎝ ⎠ ⎠

(3.37)

⎞ ⎟. ⎟ ⎠

ȼɵɫɨɬɚ ɝɨɥɨɜɤɢ ɡɭɛɚ ɞɨɥɛɹɤɚ ɩɨ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ d h a

= 0

a

−d

0 2 cos γ

0

(3.38)

. ɜ

ɉɨɥɧɚɹ ɜɵɫɨɬɚ ɡɭɛɚ ɞɨɥɛɹɤɚ h = h + 0,3m. 0 Ȼɨɤɨɜɨɣ ɡɚɞɧɢɣ ɭɝɨɥ ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɰɢɥɢɧɞɪɟ tgα ⋅ tgα ɜ α = arctg . ɛɨɤ − tgγ ⋅ tgα ɜ

(3.39)

(3.40)

Ʉɨɪɪɢɝɢɪɨɜɚɧɧɵɣ ɬɨɪɰɨɜɵɣ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɞɨɥɛɹɤɚ ɩɪɢ ɲɥɢɮɨɜɚɧɢɢ ɟɝɨ ɡɭɛɶɟɜ (ɩɨɹɜɥɹɟɬɫɹ ɜ ɫɜɹɡɢ ɫ ɧɚɥɢɱɢɟɦ ɩɟɪɟɞɧɟɝɨ ɭɝɥɚ Ȗ): – ɞɥɹ ɩɪɹɦɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ (3.4) ); α = arctg (tgα + tgγ ⋅ tgα ɢ ɛɨɤ – ɞɥɹ «ɨɫɬɪɨɣ» (ɩɨɡɢɬɢɜɧɨɣ) ɫɬɨɪɨɧɵ ɡɭɛɚ ɭ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ *) α

ɨɫɬ

= arctg

(tgα + tgγ ⋅ tgα

) ⋅ cos α ɛɨɤ ɛɨɤ ; cos(β + α ) ɛɨɤ

(3.42)

_____________________________

*) Ⱦɨɥɛɹɤ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧ ɞɥɹ ɧɚɪɟɡɚɧɢɹ ɡɭɛɶɟɜ ɲɟɜɪɨɧɧɵɯ ɤɨɥɟɫ ɫ ɡɚɤɪɵɬɵɦ ɲɟɜɪɨɧɨɦ. 68

– ɞɥɹ «ɬɭɩɨɣ» (ɧɟɝɚɬɢɜɧɨɣ) ɫɬɨɪɨɧɵ ɡɭɛɚ ɭ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ α

ɬɭɩ

= arctg

(tgα + tgγ ⋅ tgα

) ⋅ cos α ɛɨɤ ɛɨɤ . cos(β − α ) ɛɨɤ

(3.43)

Ⱦɢɚɦɟɬɪɵ ɨɫɧɨɜɧɵɯ ɨɤɪɭɠɧɨɫɬɟɣ ɞɨɥɛɹɤɚ ɩɪɢ ɲɥɢɮɨɜɚɧɢɢ ɩɪɨɮɢɥɹ ɟɝɨ ɡɭɛɶɟɜ: – ɞɥɹ ɩɪɹɦɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ = d ⋅ cos α ; bo ɢ 0 – ɞɥɹ «ɨɫɬɪɨɣ» ɫɬɨɪɨɧɵ ɭ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ = d ⋅ cos α d ; d

bo ɨɫɬ

0

ɨɫɬ

(3.44)

(3.45)

– ɞɥɹ «ɬɭɩɨɣ» ɫɬɨɪɨɧɵ ɭ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ

d

bo

ɬɭɩ

= d ⋅ cos α . ɬɭɩ 0

(3.46)

Ɂɚɞɧɢɣ ɭɝɨɥ ɩɪɢ ɜɟɪɲɢɧɟ ɜ ɨɫɟɜɨɦ ɫɟɱɟɧɢɢ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ tgα ɜ. α = arctg ɤ cos β

(3.47)

ɍɝɨɥ ɩɪɨɮɢɥɹ ɜ ɝɪɚɧɢɱɧɨɣ ɬɨɱɤɟ ɩɪɨɮɢɥɹ ɡɭɛɚ ɞɨɥɛɹɤɚ ɢ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɩɪɨɮɢɥɹ ɜ ɷɬɨɣ ɬɨɱɤɟ ⎡ 4 ⋅ (h* − h* − x ) ⋅ cos β ⎤ ⎥, ⎢ l a 0 α = arctg tgα − ⎥ ⎢ t l z ⋅ sin 2α 0 t 0 ⎥⎦ ⎢⎣ *

(3.48)

ɝɞɟ h l – ɤɨɷɮɮɢɰɢɟɧɬ ɝɪɚɧɢɱɧɨɣ ɜɵɫɨɬɵ ɡɭɛɚ ɤɨɥɟɫɚ. h*l = 2 ɢɥɢ ɞɪɭɝɨɟ

ɡɧɚɱɟɧɢɟ. (3.49)

hl* − ha* − x0 ⋅ m. ρ l0 = 0,5d 0 ⋅ sin α t − sin 2α t

ɍɝɨɥ ɪɚɡɜɟɪɧɭɬɨɫɬɢ ɜ ɝɪɚɧɢɱɧɨɣ ɬɨɱɤɟ ɩɪɨɮɢɥɹ (ɫɦ. ȽɈɋɌ 9323-79, ɫ.42) ɜ ɝɪɚɞɭɫɚɯ .ν

l 0

= (invα

l 0

(3.50)

+ α , ɪɚɞ) ⋅ 80° / π. l 0

69

Ɋɚɡɧɨɫɬɶ ɭɝɥɨɜ ɪɚɡɜɟɪɧɭɬɨɫɬɢ ɧɚ ɜɟɪɲɢɧɟ ɡɭɛɚ ɢ ɜ ɝɪɚɧɢɱɧɨɣ ɬɨɱɤɟ ɩɪɨɮɢɥɹ ɜ ɝɪɚɞɭɫɚɯ δν

al

=α 0

al

−ν 0

l

.

(3.5)

0

ɂɫɯɨɞɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɜɞɨɥɶ ɡɭɛɚ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ

A' = A / cos β .

(3.52)

Ɂɚɞɧɢɣ ɭɝɨɥ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ: – ɞɥɹ ɩɪɹɦɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ

α = arctg (tgα ⋅ sin α ); n ɜ ɢ – ɞɥɹ «ɨɫɬɪɨɣ» ɫɬɨɪɨɧɵ ɭ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ α

n

ɨɫɬ

(3.53)

(3.54)

= arctg (tgα ⋅ sin α ); ɜ ɨɫɬ

– ɞɥɹ «ɬɭɩɨɣ» ɫɬɨɪɨɧɵ ɭ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ α

n

ɬɭɩ

). = arctg (tgα ⋅ sin α ɜ ɬɭɩ

(3.55) Ɍɚɛɥɢɰɚ 3.2.

ɇɨɦɢɆɨɧɚɥɶɧɵɣ ɞɭɥɶ ɞɢɚɦɟɬɪ m, ɦɦ ɞɨɥɛɹɤɚ d0, ɦɦ 80 –5 –,75 00 2–5 6–8 2–4,5 25 5–0 6–7 60 8–0 200 8–2

Ɋɚɡɦɟɪɵ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ, ɦɦ dɨɬɜ b1 3,75 8 44,45 8 44,45 0 44,45 2 44,45 0 44,45 4 88,9 6 88,9 20 0,6 25

Ɋɚɡɦɟɪɵ ɜɵɬɨɱɤɢ, ɦɦ Ⱦ 50 70 70 70 80 80 20 20 40

b2 9 9 3 5 7 2 26

70

Ⱦɢɚɦɟɬɪ ɛɨɤɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɞɥɹ ɡɚɤɪɟɩɥɟɧɢɹ Ⱦ2 0,7da0 ɫ ɨɤɪɭɝɥɟɧɢɟɦ ɫ ɤɪɚɬɧɨɫɬɶɸ 5 ɦɦ ɜ ɦɟɧɶɲɭɸ ɫɬɨɪɨɧɭ

ȼɵɫɨɬɚ ɞɨɥɛɹɤɚ (ɫɩɪɚɜɨɱɧ.)

ȼ 2–7 7 20 22 22–24 28 30 32 40

Ɋɢɫ. 3.. Ⱦɨɥɛɹɤɢ: ɚ) ɞɢɫɤɨɜɵɣ; ɛ) ɱɚɲɟɱɧɵɣ 7

Ɉɫɬɚɥɶɧɵɟ ɤɨɧɫɬɪɭɤɬɢɜɧɵɟ ɩɚɪɚɦɟɬɪɵ ɧɚɡɧɚɱɚɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫ.3., ɢ ɬɚɛɥ. 3.2 ɞɥɹ ɞɢɫɤɨɜɵɯ ɞɨɥɛɹɤɨɜ, ɪɢɫ.3.,ɛ ɢ ɬɚɛɥ.3.3 – ɞɥɹ ɱɚɲɟɱɧɵɯ ɞɨɥɛɹɤɨɜ. Ⱦɥɹ ɢɡɝɨɬɨɜɥɟɧɢɹ ɤɨɥɟɫ ɜɧɟɲɧɟɝɨ ɡɚɰɟɩɥɟɧɢɹ ɱɚɲɟɱɧɵɣ ɞɨɥɛɹɤ ɩɪɢɦɟɧɹɟɬɫɹ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɟɫɥɢ ɧɟɥɶɡɹ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɢɫɤɨɜɵɣ ɞɨɥɛɹɤ, ɬ.ɟ. ɤɨɝɞɚ ɝɚɣɤɚ, ɩɪɢɦɟɧɹɟɦɚɹ ɞɥɹ ɡɚɤɪɟɩɥɟɧɢɹ ɞɨɥɛɹɤɚ, ɦɟɲɚɟɬ ɟɝɨ ɪɚɛɨɬɟ. ɗɬɨ ɧɚɛɥɸɞɚɟɬɫɹ, ɧɚɩɪɢɦɟɪ, ɩɪɢ ɡɭɛɨɞɨɥɛɥɟɧɢɢ ɞɜɭɯɜɟɧɰɨɜɵɯ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ. Ɍɚɛɥɢɰɚ 3.3. ɇɨɦɢɧɚɥɶɧɵɣ ɞɢɚɦɟɬɪ ɞɨɥɛɹɤɚ d0, ɦɦ 80

00

Ɋɚɡɦɟɪɵ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ, ɦɦ dɨɬɜ b1 –,5 3,75 8 ,75–2,5 3,75 0 2,5–3,5 3,75 0 –,5 44,45 8 ,75–4,25 44,45 2 4,5–6,5 44,45 2 Ɇɨɞɭɥɶ m, ɦɦ

Ⱦɢɚɦɟɬɪ ɫɬɭɩɢɰɵ Ⱦ2 64 64 60 80 80 72

ȾɢɚȾɥɢɧɚ ɦɟɬɪ ɡɭɛɶɟɜ, ɦɦ ɜɵɬɨɱɤɢ, ɦɦ Ⱦ Ⱦ1 ȼ (ɫɩɪɚɜ.) 50 56 0 50 56 3 50 56 5 63 70 5 63 70 8 63 70 20

ȼɵɫɨɬɚ ɞɨɥɛɹɤɚ (ɫɩɪɚɜɨɱɧ.) ɇ 28 30 30 30 32 34

3.3. Ⱦɨɩɨɥɧɢɬɟɥɶɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɪɚɡɪɚɛɨɬɤɢ ɪɚɛɨɱɟɝɨ ɱɟɪɬɟɠɚ ɡɭɛɨɪɟɡɧɨɝɨ ɞɨɥɛɹɤɚ Ɋɚɛɨɱɢɣ ɱɟɪɬɟɠ ɞɨɥɛɹɤɚ ɜɵɩɨɥɧɹɟɬɫɹ ɜ ɦɚɫɲɬɚɛɟ :. ȼɢɞɵ, ɪɚɡɪɟɡɵ ɢ ɫɟɱɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɵ ɜ ɛóɥɶɲɟɦ ɦɚɫɲɬɚɛɟ. Ⱦɨɥɛɹɤɢ ɢɡɝɨɬɚɜɥɢɜɚɸɬɫɹ ɢɡ ɛɵɫɬɪɨɪɟɠɭɳɢɯ ɫɬɚɥɟɣ Ɋ6Ɇ5, Ɋ6Ɇ5Ʉ5, Ɋ9Ʉ5, Ɋ9Ʉ0 ȽɈɋɌ 9265-73. Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ɞɨɥɛɹɤɚ ɡɚɜɢɫɢɬ ɨɬ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ ɤɨɥɟɫɚ: ɤɥ. ȺȺ – ɞɥɹ 6-ɣ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ, ɤɥ. Ⱥ – ɞɥɹ 7-ɣ, ɤɥ. ȼ – ɞɥɹ 8-ɣ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ. ȼ ɜɟɪɯɧɟɦ ɩɪɚɜɨɦ ɭɝɥɭ ɮɨɪɦɚɬɚ ɱɟɪɬɟɠɚ ɭɤɚɡɵɜɚɟɬɫɹ ɜɟɥɢɱɢɧɚ ɦɢɤɪɨɧɟɪɨɜɧɨɫɬɟɣ Ra 2,5 ɜɫɟɯ ɨɫɬɚɥɶɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɞɨɥɛɹɤɚ, ɤɪɨɦɟ ɬɟɯ, ɧɚ ɤɨ-

72

ɬɨɪɵɯ ɧɚ ɱɟɪɬɟɠɟ ɞɨɥɠɧɚ ɛɵɬɶ ɩɪɨɫɬɚɜɥɟɧɚ ɲɟɪɨɯɨɜɚɬɨɫɬɶ ɜ ɦɢɤɪɨɦɟɬɪɚɯ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 3.4. ɉɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɪɚɡɦɟɪɨɜ ɞɨɥɛɹɤɚ ɧɟ ɞɨɥɠɧɵ ɛɵɬɶ ɛɨɥɟɟ ɭɤɚɡɚɧɧɵɯ ɜ ɬɚɛɥ. 3.5, 3.6, 3.7 ɢ 3.8. ɇɚ ɪɚɛɨɱɟɦ ɱɟɪɬɟɠɟ ɩɪɢ ɩɨɦɨɳɢ ɭɫɥɨɜɧɵɯ ɨɛɨɡɧɚɱɟɧɢɣ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ȽɈɋɌ 2308-79 ɞɨɥɠɧɵ ɛɵɬɶ ɭɤɚɡɚɧɵ: – ɨɬɤɥɨɧɟɧɢɟ ɨɬ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɫɬɢ ɜɧɟɲɧɟɣ ɨɩɨɪɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 3.9; – ɨɬɤɥɨɧɟɧɢɟ ɨɬ ɩɚɪɚɥɥɟɥɶɧɨɫɬɢ ɨɩɨɪɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 3.0; – ɬɨɪɰɨɜɨɟ ɛɢɟɧɢɟ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 3.; – ɛɢɟɧɢɟ ɨɤɪɭɠɧɨɫɬɢ ɜɟɪɲɢɧ ɡɭɛɶɟɜ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 3.2; – ɪɚɞɢɚɥɶɧɨɟ ɛɢɟɧɢɟ ɡɭɛɱɚɬɨɝɨ ɜɟɧɰɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 3.3. Ɍɚɛɥɢɰɚ 3.4. ɇɚɢɦɟɧɨɜɚɧɢɟ ɩɨɜɟɪɯɧɨɫɬɢ ɉɟɪɟɞɧɢɟ ɢ ɡɚɞɧɢɟ ɩɨɜɟɪɯɧɨɫɬɢ ɡɭɛɶɟɜ Ɉɩɨɪɧɚɹ ɩɨɜɟɪɯɧɨɫɬɶ ɉɨɫɚɞɨɱɧɵɟ ɨɬɜɟɪɫɬɢɹ ȼɧɭɬɪɟɧɧɹɹ ɨɩɨɪɧɚɹ ɩɨɜɟɪɯɧɨɫɬɶ

Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ, Ⱥ ȼ ȺȺ, Ⱥ, ȼ ȺȺ Ⱥ, ȼ ȺȺ, Ⱥ, ȼ

ɒɟɪɨɯɨɜɚɬɨɫɬɶ Ra, ɦɤɦ 0,4 0,4 0,2 0,2 0,2 0,8 Ɍɚɛɥɢɰɚ 3.5.


ɇɨɦɢɧɚɥɶɧɵɣ ɞɟɥɢɬɟɥɶɧɵɣ ɞɢɚɦɟɬɪ d0, ɦɦ


Ⱦɢɚɦɟɬɪ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ dɨɬɜ

Ⱦɨ 50 ɋɜ. 50 ɞɨ 20 Ⱦɨ 50 ɋɜ. 50 ɞɨ 20

ȺȺ, Ⱥ ȺȺ, Ⱥ

73

Ɇɨɞɭɥɶ m, ɦɦ Ɉɬ ɋɜ. ɋɜ. ɋɜɵɞɨ 3,5 3,5 ɞɨ 6,5 ɲɟ 0 6,5 ɞɨ 0 Ⱦɨɩɭɫɤ, ɦɤɦ +5 – – +6 – – + 0



Ɇɨɞɭɥɶ m, ɦɦ Ⱦɥɹ ɜɫɟɯ ɦɨɞɭɥɟɣ ± 5' ± 8' ± 2' ± 3' ± 5'

ȺȺ Ⱥ ȼ ȺȺ Ⱥ, ȼ

ɉɟɪɟɞɧɢɣ ɭɝɨɥ Ȗ Ɂɚɞɧɢɣ ɭɝɨɥ Įɜ

Ɍɚɛɥɢɰɚ 3.7 ɇɚɢɦɟɧɨɜɚɧɢɟ ɩɚɪɚɦɟɬɪɚ


Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ Ɉɬ ɞɨ 2

Ⱦɢɚɦɟɬɪ ɨɤɪɭɠɧɨɫɬɢ ɜɟɪɲɢɧ ɡɭɛɶɟɜ dɚɨ

ȺȺ Ⱥ ȼ

ɋɜ. 2 ɞɨ ɋɜ. 3,5 ɞɨ ɋɜ. 6,5 ɞɨ 3,5 6,5 0 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɤɦ ± 320 ± 400 ± 500 ± 320 ± 400 ± 500 ± 400 ± 500 Ɍɚɛɥɢɰɚ 3.8.



Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ Ɉɬ ɞɨ 2

ȼɵɫɨɬɚ ɝɨɥɨɜɤɢ ɡɭɛɚ hɚɨ

ȺȺ, Ⱥ, ȼ

ɋɜ. 2 ɋɜ. 3,5 ɋɜ. 6,5 ɋɜɵɲɟ ɞɨ 3,5 ɞɨ 6,5 ɞɨ 0 0 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɤɦ

± 8

± 25

± 32

± 40

± 50


ɉɟɪɩɟɧɞɢɤɭɥɹɪɧɨɫɬɶ ɜɧɟɲɧɟɝɨ ɨɩɨɪɧɨɝɨ ɬɨɪɰɚ ɢ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ŏ



ɋɜ. 50 ɞɨ 20

ȺȺ Ⱥ ȼ ȺȺ Ⱥ

ɋɜ. 20 ɞɨ 200

ȼ

Ɇɨɞɭɥɶ m, ɦɦ Ɉɬ ɋɜ. 2 ɋɜ. 3,5 ɋɜ. 6,5 ɋɜɵ ɞɨ 6,5 ɞɨ 0 ɲɟ ɞɨ ɞɨ 0 3,5 2 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɤɦ 3 4 4 4 – 5 6 6 6 – 8 0 0 0 – – – 5 5 5 – – 8 8 8 –

74

–

2

2

2

Ɍɚɛɥɢɰɚ 3.0. ɇɚɢɦɟɧɨɜɚɧɢɟ ɨɬɤɥɨɧɟɧɢɹ

ɇɟɩɚɪɚɥɥɟɥɶɧɨɫɬɶ ɨɩɨɪɧɵɯ ɬɨɪɰɨɜ //


ɋɜ. 50 ɞɨ 25 ɋɜ. 25 ɞɨ 200


ȺȺ Ⱥ ȼ ȺȺ Ⱥ ȼ

Ɇɨɞɭɥɶ m, ɦɦ Ɉɬ ɋɜ. 2 ɋɜ. ɋɜ. ɋɜɵ ɞɨ ɞɨ 3,5 ɞɨ 6,5 ɞɨ ɲɟ 2 3,5 6,5 0 0 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɤɦ 3 4 5 6 8 0 – 5 6 – 8 – 2 Ɍɚɛɥɢɰɚ 3..

ɇɚɢɦɟɧɨɜɚɧɢɟ ɨɬɤɥɨɧɟɧɢɹ

Ɍɨɪɰɟɜɨɟ ɛɢɟɧɢɟ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ (ɢɡɦɟɪ. ɧɚ ɞɟɥɢɬ. ɨɤɪɭɠ. ɢɥɢ ɛɥɢɡɤɨɣ ɤ ɧɟɣ)


ɋɜ. 50 ɞɨ 25 ɋɜ. 25 ɞɨ 200


ȺȺ Ⱥ ȼ

Ɇɨɞɭɥɶ m, ɦɦ Ɉɬ ɋɜ. 2 ɋɜ. ɋɜ. ɋɜɵ ɞɨ ɞɨ 3,5 3,5 ɞɨ 6,5 ɲɟ 0 2 6,5 ɞɨ 0 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɤɦ 2 – 6 – 25 –

ȺȺ Ⱥ ȼ

– – –

20 28 40 Ɍɚɛɥɢɰɚ 3.2.

ɇɚɢɦɟɧɨɜɚɧɢɟ ɨɬɤɥɨɧɟɧɢɹ

Ȼɢɟɧɢɟ ɨɤɪɭɠɧɨɫɬɢ ɜɟɪɲɢɧɵ


ɋɜ. 50 ɞɨ 25

ɋɜ. 25 ɞɨ 200


ȺȺ Ⱥ ȼ ȺȺ Ⱥ ȼ 75

Ɇɨɞɭɥɶ m, ɦɦ ɋɜɵɋɜ. ɋɜ. ɋɜ. 2 3,5 ɞɨ 6,5 ɞɨ ɲɟ 0 ɞɨ 0 6,5 3,5 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɤɦ – 2 0 – 20 6 – 32 25 20 6 32 25 – 50 40 – –

Ɉɬ ɞɨ 2

Ɍɚɛɥɢɰɚ 3.3. ɇɚɢɦɟɧɨɜɚɧɢɟ ɨɬɤɥɨɧɟɧɢɹ


Ɋɚɞɢɚɥɶɧɨɟ ɛɢɟɧɢɟ ɡɭɛɱɚɬɨɝɨ ɜɟɧɰɚ

ɋɜ. 50 ɞɨ 25 ɋɜ. 25 ɞɨ 200


ȺȺ Ⱥ ȼ ȺȺ Ⱥ ȼ

Ɇɨɞɭɥɶ m, ɦɦ Ɉɬ ɋɜ. 2 ɋɜ. ɋɜ. ɋɜɵ ɞɨ 3,5 ɞɨ 6,5 ɲɟ 0 ɞɨ 3,5 6,5 ɞɨ 0 2 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɤɦ 2 4 – 6 8 20 – 24 26 32 20 – 8 20 – 24 – 36 40

ȼ ɬɟɯɧɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɹɯ ɞɨɥɠɧɨ ɛɵɬɶ ɭɤɚɡɚɧɨ: . ɇRCɷ 63...65. 2. ɇɚ ɜɫɟɯ ɩɨɜɟɪɯɧɨɫɬɹɯ ɞɨɥɛɹɤɚ ɧɟ ɞɨɥɠɧɨ ɛɵɬɶ ɬɪɟɳɢɧ, ɡɚɛɨɢɧ, ɜɵɤɪɨɲɟɧɧɵɯ ɦɟɫɬ, ɡɚɭɫɟɧɰɟɜ ɢ ɫɥɟɞɨɜ ɤɨɪɪɨɡɢɢ 3. ɉɨɝɪɟɲɧɨɫɬɶ ɩɪɨɮɢɥɹ ɡɭɛɚ … (ɬɚɛɥ.3.4) Ɍɚɛɥɢɰɚ 3.4 Ɇɨɞɭɥɶ m, ɦɦ

Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ Ɉɬ ɞɨ 2 ȺȺ Ⱥ ȼ

0,003 0,004 0,008

ɋɜ. 2 ɋɜ. 3,5 ɋɜ. 6,5 ɞɨ 3,5 ɞɨ 6,5 ɞɨ 0 ɋɜɵɲɟ 0 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɦ 0,004 0,006 0,005 0,007 0,0 0,0 0,02 0,06 0,02

4. Ɋɚɡɧɨɫɬɶ ɫɨɫɟɞɧɢɯ ɨɤɪɭɠɧɵɯ ɲɚɝɨɜ ɡɭɛɶɟɜ … (ɬɚɛɥ. 3.5)

76

Ɍɚɛɥɢɰɚ 3.5 Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ

Ɇɨɞɭɥɶ m, ɦɦ Ɉɬ ɞɨ 2

ȺȺ Ⱥ ȼ

0,003 0,005 0,008

ɋɜ. 2 ɋɜ. 3,5 ɋɜ. 6,5 ɞɨ 3,5 ɞɨ 6,5 ɞɨ 0 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɦ 0,004 0,006 0,0

ɋɜɵɲɟ 0 0,006 0,008 0,02

5. ɇɚɤɨɩɥɟɧɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɨɤɪɭɠɧɨɝɨ ɲɚɝɚ ɡɭɛɶɟɜ ... (ɬɚɛɥ. 3.6) Ɍɚɛɥɢɰɚ 3.6 Ɇɨɞɭɥɶ m, ɦɦ

Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ Ɉɬ ɞɨ 2 ȺȺ Ⱥ ȼ

0,003 0,04 0,02

ɋɜ. 2 ɋɜ. 3,5 ɋɜ. 6,5 ɞɨ 3,5 ɞɨ 6,5 ɞɨ 0 ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɦ 0,0 0,08 0,024 0,03

ɋɜɵɲɟ 0 0,04 0,022 0,036

6. Ʉɨɧɭɫɧɨɫɬɶ ɢ ɨɜɚɥɶɧɨɫɬɶ ɨɬɜ. ∅ (ɪɚɡɦɟɪ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ) ... (0,5 ɞɨɩɭɫɤɚ ɧɚ ɞɢɚɦɟɬɪ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ). ɇɟ ɞɨɩɭɫɤɚɸɬɫɹ ɡɚɜɚɥɵ ɤɪɚɟɜ ɨɬɜɟɪɫɬɢɹ ∅ ... ɡɚ ɩɪɟɞɟɥɵ 0,25 ɟɝɨ ɞɥɢɧɵ. 7. Ⱦɢɚɦɟɬɪ ɨɫɧɨɜɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɩɢɪɚ Ⱦɤ = ... (ɞɥɹ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ ɩɪɢɜɨɞɹɬɫɹ ɞɚɧɧɵɟ ɞɥɹ ɲɥɢɮɨɜɚɧɢɹ ɢ ɫɬɨɪɨɧɵ ɡɭɛɶɟɜ). 8. ɇɟɭɤɚɡɚɧɧɵɟ ɩɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɪɚɡɦɟɪɨɜ: ɨɬɜ. ɇ14, ɜɚɥɨɜ JT4 h14, ɩɪɨɱɢɯ ± 2 9. Ɇɚɪɤɢɪɨɜɚɬɶ m = ... z0 = ....ɤɥ.... β = ... Pz = ... (ɞɥɹ ɤɨɫɨɡɭɛɨɝɨ ɞɨɥɛɹɤɚ) Ɋ6Ɇ5.

77

4. ɊȺɋɑȿɌ ɂ ɉɊɈȿɄɌɂɊɈȼȺɇɂȿ ȾɂɋɄɈȼɕɏ ɒȿȼȿɊɈȼ Ⱦɢɫɤɨɜɵɟ ɲɟɜɟɪɵ ɩɪɢɦɟɧɹɸɬɫɹ ɞɥɹ ɱɢɫɬɨɜɨɣ ɨɛɪɚɛɨɬɤɢ ɰɢɥɢɧɞɪɢɱɟɫɤɢɯ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ. ɉɪɢɧɰɢɩ ɢɯ ɪɚɛɨɬɵ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɬɧɨɫɢɬɟɥɶɧɨɦ ɩɪɨɫɤɚɥɶɡɵɜɚɧɢɢ ɜɞɨɥɶ ɡɭɛɶɟɜ ɲɟɜɟɪɚ ɤɨɥɟɫɚ. ɂ ɬɚɤ ɤɚɤ ɧɚ ɡɭɛɶɹɯ ɲɟɜɟɪɚ ɢɡɝɨɬɨɜɥɟɧɵ ɪɟɠɭɳɢɟ ɷɥɟɦɟɧɬɵ (ɪɟɡɰɵ), ɬɨ ɩɪɨɢɫɯɨɞɢɬ ɫɪɟɡɚɧɢɟ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɡɭɛɶɟɜ ɤɨɥɟɫɚ ɬɨɧɤɢɯ ɫɬɪɭɠɟɤ. ɒɟɜɟɪ ɪɚɛɨɬɚɟɬ ɬɨɥɶɤɨ ɷɜɨɥɶɜɟɧɬɧɨɣ ɱɚɫɬɶɸ ɡɭɛɚ. ɉɨɷɬɨɦɭ ɩɪɨɮɢɥɶ ɡɭɛɶɟɜ ɤɨɥɟɫɚ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ ɞɨɥɠɟɧ ɛɵɬɶ ɦɨɞɢɮɢɰɢɪɨɜɚɧ: ɢɦɟɬɶ ɫɪɟɡ ɭ ɜɟɪɲɢɧɵ ɢ ɩɨɞɪɟɡ ɭ ɨɫɧɨɜɚɧɢɹ ɡɭɛɚ. 4.1. Ɋɚɫɱɟɬ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɫɪɟɞɧɟɦɨɞɭɥɶɧɵɯ ɢ ɦɟɥɤɨɦɨɞɭɥɶɧɵɯ ɲɟɜɟɪɨɜ ɍɝɨɥ ɫɤɪɟɳɢɜɚɧɢɹ ɨɫɟɣ ɲɟɜɟɪɚ ɢ ɤɨɥɟɫɚ ĳ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ 8÷20°, ɜ ɫɪɟɞɧɟɦ ĳ = 5°. ɍɝɨɥ ɧɚɤɥɨɧɚ ɡɭɛɶɟɜ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɲɟɜɟɪɚ (ɨɧ ɧɟ ɞɨɥɠɟɧ ɩɪɟɜɵɲɚɬɶ 30°) ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ: β = β ± ϕ, (4.) 0 ɝɞɟ ɡɧɚɤ «+» ɨɬɧɨɫɢɬɫɹ ɤ ɪɚɡɧɨɢɦɟɧɧɨɦɭ ɧɚɩɪɚɜɥɟɧɢɸ ɡɭɛɶɟɜ ɲɟɜɟɪɚ ɢ

ɤɨɥɟɫɚ (ɩɪɚɜɨɟ ɢ ɥɟɜɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɡɭɛɶɟɜ), « - » – ɤ ɨɞɧɨɢɦɟɧɧɨɦɭ. ɇɚɩɪɚɜɥɟɧɢɟ ɡɭɛɚ ɤɨɥɟɫɚ ɢɡɜɟɫɬɧɨ. Ɂɚɞɚɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ ɡɭɛɚ ɲɟɜɟɪɚ (ɞɥɹ ɩɪɹɦɨɡɭɛɨɝɨ ɤɨɥɟɫɚ ɜɫɟɝɞɚ ɩɪɚɜɨɟ ɧɚɩɪɚɜɥɟɧɢɟ) ɢ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ȕ0. ȿɫɥɢ ɭɝɨɥ ɨɤɚɡɚɥɫɹ ɦɟɧɶɲɟ 0° ɢɥɢ ɛɨɥɶɲɟ 30°, ɬɨ ɫɥɟɞɭɟɬ ɢɡɦɟɧɢɬɶ ɧɚɩɪɚɜɥɟɧɢɟ ɡɭɛɚ ɲɟɜɟɪɚ ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɟ, ɚ ɡɚɬɟɦ ɭɠɟ ɨɤɨɧɱɚɬɟɥɶɧɨ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ȕ0. ȿɫɥɢ ɩɪɢ ɪɚɫɱɟɬɟ ɩɨɥɭɱɢɬɫɹ ɡɧɚɱɟɧɢɟ ɦɟɧɶɲɟ 5°, ɬɨ ɦɨɠɧɨ ɩɪɢɧɹɬɶ ȕ0=0° (ɬɚɤɨɣ ɲɟɜɟɪ ɥɟɝɱɟ ɢɡɝɨɬɨɜɢɬɶ ɢ ɩɟɪɟɬɚɱɢɜɚɬɶ). Ɂɚɬɟɦ ɫɥɟɞɭɟɬ ɩɟɪɟɫɱɢɬɚɬɶ ɭɝɨɥ ĳ:

78

ϕ = β0 ± β.

(4.2)

Ɂɧɚɱɟɧɢɟ ĳ ɞɨɥɠɧɨ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɭɫɥɨɜɢɸ: 8° ĳ 20°. ɑɢɫɥɨ ɡɭɛɶɟɜ ɫɪɟɞɧɟɦɨɞɭɥɶɧɨɝɨ ɲɟɜɟɪɚ (m > ,75 ɦɦ) ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ: z = 0

(d

ao max

− 3m) ⋅ cos β m

0,

(4.3)

ɝɞɟ daomax – ɦɚɤɫɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɧɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɲɟɜɟɪɚ. Ɉɧ ɩɪɢɧɢɦɚɟɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɦɨɞɟɥɢ ɫɬɚɧɤɚ, ɧɚ ɤɨɬɨɪɨɦ ɛɭɞɟɬ ɩɪɨɢɡɜɨɞɢɬɶɫɹ ɨɛɪɚɛɨɬɤɚ ɤɨɥɟɫ (ɬɚɛɥ. 4.). Ɍɚɛɥɢɰɚ 4.. Ɇɨɞɟɥɶ ɫɬɚɧɤɚ 572 57 578 574 575 5702 576 5A74 577 5706 5708 5Ȼ702ȼ 5702ȼ 5Ⱥ703 570

Ⱦɢɚɦɟɬɪ ɩɨɫɚɞɨɱɧɨɣ ɲɟɣɤɢ ɲɩɢɧɞɟɥɹ d, ɦɦ 3,75 63,5 63,5 63,5 65 63,5 63,5 63,5 63,5 76,2 76,2 63,5 63,5 63,5 63,5

ɒɟɜɟɪ daomax 20 88 88 240 20 300 88 240 300 350 350 250 240 300 20

bmax 32 40 40 40 40 40 40 40 00 70 70 40 40 40 40

ɉɨɞɫɱɢɬɚɧɧɨɟ ɡɧɚɱɟɧɢɟ z0 ɭɬɨɱɧɹɟɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɱɢɫɥɨɦ ɞɟɥɟɧɢɣ ɞɢɫɤɚ ɡɭɛɨɲɥɢɮɨɜɚɥɶɧɨɝɨ ɫɬɚɧɤɚ: 23, 29, 3, 37, 4, 43, 47, 53, 6, 67, 73, 83, 0, 03. ɉɨɫɥɟ ɜɵɛɨɪɚ ɱɢɫɥɚ z0 ɢɡ ɪɹɞɚ ɨɩɪɟɞɟɥɹɟɦ m⋅ z 0 . d = 0 cos β 0

(4.4)

79

ɉɨɞɫɱɢɬɚɧɧɨɟ ɡɧɚɱɟɧɢɟ d0 ɧɟ ɞɨɥɠɧɨ ɩɪɟɜɵɲɚɬɶ ɨɞɧɨɝɨ ɢɡ ɡɧɚɱɟɧɢɣ ɫɬɚɧɞɚɪɬɧɨɝɨ ɪɹɞɚ: 85, 80, 250. Ɍɨɪɰɨɜɵɣ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɲɟɜɟɪɚ d

t

= arctg 0

tgα . cos β 0

(4.5)

Ⱦɢɚɦɟɬɪ ɨɫɧɨɜɧɨɣ ɨɤɪɭɠɧɨɫɬɢ (4.6) = d ⋅ cos α . b t 0 0 0 Ɉɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɱɟɧɢɟ ɞɢɚɦɟɬɪɚ ɨɫɧɨɜɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɩɢɪɚ Ⱦɤ, ɩɪɢ d

ɩɨɦɨɳɢ ɤɨɬɨɪɨɝɨ ɛɭɞɭɬ ɲɥɢɮɨɜɚɬɶɫɹ ɡɭɛɶɹ ɲɟɜɟɪɚ. Ʌɭɱɲɟ ɜɫɟɝɨ, ɤɨɝɞɚ Ⱦɤ = d0 ; ɢɥɢ Ⱦɤ § d0 (ɧɨ Ⱦɤ > db0). Ʉɪɨɦɟ ɬɨɝɨ, Ⱦɤ ɞɨɥɠɟɧ ɛɵɬɶ ɪɚɜɟɧ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɡɧɚɱɟɧɢɣ ɪɹɞɚ: 75; 76,2; 77; 88,9; 99; 00; 0,6; 03; 07; 25; 27; 42; 50; 62; 64; 7; 78; 80; 98; 202; 225; 250. ɍɝɨɥ ɭɫɬɚɧɨɜɤɢ ɫɚɥɚɡɨɤ ɡɭɛɨɲɥɢɮɨɜɚɥɶɧɨɝɨ ɫɬɚɧɤɚ d b α = arccos 0 . ɭɫɬ Ⱦ ɤ

(4.7)

Ⱦɥɹ ɪɚɜɧɨɦɟɪɧɨɝɨ ɢɡɧɨɫɚ ɲɥɢɮɨɜɚɥɶɧɨɝɨ ɤɪɭɝɚ ɧɟɨɛɯɨɞɢɦɨ ɜɵɞɟɪɠɚɬɶ ɭɫɥɨɜɢɟ: (4.8) ≥ (α − 6°). (α + °) ≥ α t

0

ɭɫɬ

t

0

ȿɫɥɢ ɷɬɨ ɭɫɥɨɜɢɟ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɭɦɟɧɶɲɚɟɦ daomax, ɧɨ ɧɟ ɛɨɥɟɟ ɱɟɦ ɧɚ 30%, ɢ ɩɨɜɬɨɪɹɟɦ ɪɚɫɱɟɬ ɫ ɮɨɪɦɭɥɵ 4.3. ȿɫɥɢ ɢ ɩɨɫɥɟ ɷɬɨɝɨ ɭɫɥɨɜɢɟ ɩɨ ɭɝɥɭ Įɭɫɬ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɬɪɟɛɭɟɬɫɹ ɢɡɝɨɬɨɜɢɬɶ ɫɩɟɰɢɚɥɶɧɵɣ ɤɨɩɢɪ ɤ ɡɭɛɨɲɥɢɮɨɜɚɥɶɧɨɦɭ ɫɬɚɧɤɭ, ɞɢɚɦɟɬɪ ɤɨɬɨɪɨɝɨ Ⱦɤ = d0 (d0 ɢɡ ɩɟɪɜɨɝɨ ɪɚɫɱɟɬɚ). Ɇɨɠɧɨ ɩɪɟɞɭɫɦɨɬɪɟɬɶ ɲɥɢɮɨɜɚɧɢɟ ɡɭɛɶɟɜ ɲɟɜɟɪɚ ɧɚ ɫɬɚɧɤɟ, ɩɨɡɜɨɥɹɸɳɟɦ ɩɪɨɢɡɜɨɞɢɬɶ ɲɥɢɮɨɜɚɧɢɟ ɡɭɛɶɟɜ ɲɟɜɟɪɚ ɫ ɥɸɛɵɦ ɱɢɫɥɨɦ ɡɭɛɶɟɜ. ɑɢɫɥɨ ɡɭɛɶɟɜ ɦɟɥɤɨɦɨɞɭɥɶɧɨɝɨ ɲɟɜɟɪɚ (m < ,75 ɦɦ) ɨɩɪɟɞɟɥɹɟɬɫɹ (ɩɨ ȽɈɋɌ 8570-80 ɢ ȽɈɋɌ 0222-8, [2, 3]) ɩɨ ɬɚɛɥ. 4.2.

80

Ɍɚɛɥɢɰɚ 4.2. Ɇɨɞɭɥɶ m, ɦɦ 0,2 0,22 0,25 0,28 0,3 0,35 0,4 0,45 0,5 0,55 ɑɢɫɥɨ ɡɭɛɶɟɜ z0 438 396 348 32 292 246 22 92 72 54 Ɇɨɞɭɥɶ m, ɦɦ 0,6 ɑɢɫɥɨ ɡɭɛɶɟɜ z0 46

0,7 22

0,8 06

0,9 94

86

,25 ,375 67 62

,5 58

,75 53

ɍɝɨɥ ɩɨɞɴɟɦɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɪɰɚ ɧɚ ɨɫɧɨɜɧɨɦ ɰɢɥɢɧɞɪɟ ɲɟɜɟɪɚ

σ = arccos(cosα ⋅ sin β ). (4.9) 0 0 ɉɪɢɩɭɫɤ ɧɚ ɫɬɨɪɨɧɭ ɡɭɛɚ ɫɪɟɞɧɟɦɨɞɭɥɶɧɨɝɨ ɧɚ ɩɟɪɟɲɥɢɮɨɜɤɭ (ɩɟɪɟɬɨɱɤɭ ɢɧɫɬɪɭɦɟɧɬɚ) *) ǻ = 0,2 + 0,03·m.

(4.0)

ɉɪɢɩɭɫɤ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɫɯɨɞɧɨɝɨ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ a=ǻ/2.

(4.)

Ⱦɥɹ ɦɟɥɤɨɦɨɞɭɥɶɧɨɝɨ ɲɟɜɟɪɚ ǻ ɢ ɚ ɪɚɜɧɵ 0. Ɍɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɞɭɝɟ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɧɨɜɨɝɨ ɲɟɜɟɪɚ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ: ɞɥɹ m ,75 ɦɦ – Sn0 = ʌ·m - Sn1;

(4.2)

ɞɥɹ m > ,75 ɦɦ – Sn0 = ʌ·m - Sn1 + 2a .

(4.3)

Ɂɚɡɨɪ «Ʉ» ɦɟɠɞɭ ɨɤɪɭɠɧɨɫɬɶɸ ɜɟɪɲɢɧ ɡɭɛɶɟɜ ɤɨɥɟɫɚ ɢ ɨɤɪɭɠɧɨɫɬɶɸ ɜɩɚɞɢɧ ɡɭɛɶɟɜ ɲɟɜɟɪɚ: ɩɪɢ m 1,75 ɦɦ – K = 0,25 m ;

(4.4)

ɩɪɢ m > 1,75 ɦɦ – K = 0,2 m.

(4.5)

ȼɵɫɨɬɚ ɧɨɠɤɢ ɡɭɛɚ ɲɟɜɟɪɚ: ɩɪɢ m 1,75 ɦɦ ɩɪɢ m > 1,75 ɦɦ –

= h + 0,25m; a

(4.6)

Δ−a =h +K− . f a α tg 0

(4.7)

– h h

f0

________________________ *) ɉɪɢ ɤɚɠɞɨɣ ɩɟɪɟɬɨɱɤɟ ɩɨ ɩɪɨɮɢɥɸ ɡɭɛɶɟɜ ɭ ɫɪɟɞɧɟɦɨɞɭɥɶɧɨɝɨ ɲɟɜɟɪɚ ɩɪɨɢɡɜɨɞɢɬɫɹ ɲɥɢɮɨɜɚɧɢɟ ɢ ɩɨ ɧɚɪɭɠɧɨɦɭ ɰɢɥɢɧɞɪɭ, ɬ.ɟ. ɜɟɪɲɢɧ ɡɭɛɶɟɜ.

8

ȼɧɭɬɪɟɧɧɢɣ ɞɢɚɦɟɬɪ ɲɟɜɟɪɚ D

f

= d − 2h . f 0 0

(4.8)

Ⱦɥɹ ɝɚɪɚɧɬɢɢ ɢɫɩɨɥɧɟɧɢɹ ɷɜɨɥɶɜɟɧɬɧɨɝɨ ɩɪɨɮɢɥɹ ɩɨ ɜɫɟɣ ɜɵɫɨɬɟ ɡɭɛɚ ɲɟɜɟɪɚ ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ D

≥d

f

b 0

(4.9)

+ 2.

ȿɫɥɢ ɷɬɨ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɩɪɢɧɢɦɚɸɬ ɏ = 0. ȿɫɥɢ ɠɟ ɷɬɨ ɭɫɥɨɜɢɟ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɦɟɧɶɲɟɧɢɟ ɜɵɫɨɬɵ ɧɨɠɤɢ ɡɭɛɚ ɲɟɜɟɪɚ (ɭɜɟɥɢɱɟɧɢɟ ɝɨɥɨɜɤɢ ɡɭɛɚ ɲɟɜɟɪɚ): −D

d

b X = 0

f

2

+ .

(4.20)

Ɂɚɬɟɦ ɩɟɪɟɫɱɢɬɵɜɚɸɬ Sn0 ɢ Df : Sn0 = Sn0 (ɩɪɟɠɧɟɟ ɡɧɚɱɟɧɢɟ) + 2·ɏ·tgĮ ;

(4.2)

Df = Df (ɩɪɟɠɧɟɟ ɡɧɚɱɟɧɢɟ) + 2·ɏ.

(4.22)

ȼɵɫɨɬɚ ɝɨɥɨɜɤɢ ɡɭɛɚ ɲɟɜɟɪɚ: ɩɪɢ m 1,75 ɦɦ –

h a

=h 0

f

− 0,5m;

(4.23) a

+ X. ɩɪɢ m > 1,75 ɦɦ – ha = h f − 0,5m + tgα 0

(4.24)

Ⱦɢɚɦɟɬɪ ɜɵɫɬɭɩɨɜ (ɧɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ) ɲɟɜɟɪɚ d

a

= d + 2h ; a 0 0 0

(4.25)

ȼɵɫɨɬɚ ɡɭɛɚ ɲɟɜɟɪɚ d h = 0

a

−D 0

Ƚɥɭɛɢɧɚ

2

f

(4.26)

.

ɫɬɪɭɠɟɱɧɵɯ

ɤɚɧɚɜɨɤ

ɞɥɹ

ɫɪɟɞɧɟɦɨɞɭɥɶɧɵɯ

ɲɟɜɟɪɨɜ

(m > ,75 ɦɦ) (ɪɢɫ.4.) L = 0,4 + 0,1 m ;

(4.27)

82

ɨɤɪɭɝɥɢɬɶ ɫ ɤɪɚɬɧɨɫɬɶɸ 0, ɦɦ ɜ ɛɥɢɠɚɣɲɭɸ ɫɬɨɪɨɧɭ. ȿɫɥɢ L > ,2 ɦɦ, ɬɨ ɩɪɢɧɹɬɶ L = ,2 ɦɦ. ɉɪɨɜɟɪɢɬɶ ɬɨɥɳɢɧɭ ɡɭɛɚ ɧɨɜɨɝɨ ɫɪɟɞɧɟɦɨɞɭɥɶɧɨɝɨ ɲɟɜɟɪɚ ( m > ,75 ɦɦ) ɧɚ ɡɚɨɫɬɪɟɧɢɟ ɜɟɪɲɢɧɵ ɡɭɛɚ. Ⱦɥɹ ɱɟɝɨ ɨɩɪɟɞɟɥɢɬɶ: – ɭɝɨɥ ɩɪɨɮɢɥɹ ɩɪɢ ɜɟɪɲɢɧɟ ɡɭɛɚ ɧɨɜɨɝɨ ɲɟɜɟɪɚ ɜ ɬɨɪɰɨɜɨɦ ɫɟɱɟɧɢɢ d

b (4.28) 0 ; at d 0 ɚ 0 – ɭɝɨɥ ɧɚɤɥɨɧɚ ɡɭɛɶɟɜ ɲɟɜɟɪɚ ɧɚ ɧɚɪɭɠɧɨɦ ɞɢɚɦɟɬɪɟ d ⋅ tgβ a 0 0 (4.29) ; β = arctg a d 0 0 – ɬɨɥɳɢɧɭ ɡɭɛɚ ɩɨ ɧɨɪɦɚɥɢ ɧɚ ɧɚɪɭɠɧɨɦ ɞɢɚɦɟɬɪɟ ɧɨɜɨɝɨ ɲɟɜɟɪɚ α

= arccos

⎛ S n ⎜ 0 = d ⋅⎜ + invα − invα S an a ⎜ d ⋅ cos β t at 0 0 0 0 0 0 ⎝

⎞ ⎟ ⎟ ⋅ cos β a ; ⎟ 0 ⎠

(4.30)

– ɪɚɡɦɟɪ Ɋ (ɪɢɫ.4.) – ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɫɬɪɭɠɟɱɧɵɦɢ ɤɚɧɚɜɤɚɦɢ, ɩɪɨɫɬɪɨɝɚɧɧɵɦɢ ɫ ɞɜɭɯ ɫɬɨɪɨɧ ɡɭɛɚ ɲɟɜɟɪɚ 2 ⋅ L ⋅ cos β P=S

an 0

−

a

0

⎤ ⎡ cos ⎢arctg (tgα ⋅ cos β )⎥ at a ⎥ ⎢⎣ 0 0 ⎦

(4.3) .

ȿɫɥɢ Ɋ 0, ɦɦ, ɬɨ ɩɪɢɩɭɫɤ ɧɚ ɩɟɪɟɬɨɱɤɭ ɫɪɟɞɧɟɦɨɞɭɥɶɧɨɝɨ ɲɟɜɟɪɚ ɜɵɛɪɚɧ ɩɪɚɜɢɥɶɧɨ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɫɥɟɞɭɟɬ ɭɦɟɧɶɲɢɬɶ ɩɪɢɩɭɫɤ ɧɚ ɩɟɪɟɬɨɱɤɭ ɧɚ 0,·ɚ (ɚ = ɚ (ɩɪɟɠɧɟɟ ɡɧɚɱɟɧɢɟ) – 0,1·ɚ), ɢ, ɧɚɱɢɧɚɹ ɫ ɮɨɪɦɭɥɵ 4.2, ɩɟɪɟɫɱɢɬɚɬɶ ɩɚɪɚɦɟɬɪɵ ɧɨɜɨɝɨ ɲɟɜɟɪɚ. ɂ ɷɬɨ ɧɟɨɛɯɨɞɢɦɨ ɩɨɜɬɨɪɹɬɶ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɧɟ ɛɭɞɟɬ ɜɵɩɨɥɧɟɧɨ ɭɫɥɨɜɢɟ P 0, ɦɦ.

83

ɉɪɨɜɟɪɤɚ ɧɚ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɪɚɛɨɬɤɢ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ ɫ ɩɨɦɨɳɶɸ ɫɪɟɞɧɟɦɨɞɭɥɶɧɨɝɨ ɲɟɜɟɪɚ ɚ) ɧɨɜɵɦ ɲɟɜɟɪɨɦ ɇɚɱɚɥɶɧɵɣ ɞɢɚɦɟɬɪ ɧɨɜɨɝɨ ɲɟɜɟɪɚ

d'

=d + w0 0

2(Δ − a ) . tgα

(4.32)

ɍɝɨɥ ɧɚɤɥɨɧɚ ɡɭɛɶɟɜ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɧɨɜɨɝɨ ɲɟɜɟɪɚ ⎛ d 'w ⎞ ⎜ ⎟ 0 β' = arctg ⎜ ⋅ tgβ ⎟. w 0 ⎜ d0 ⎟ 0 ⎝ ⎠

ɉɪɢ

β 0 = 0° –

β'

w0

(4.33)

= 0°.

ɍɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɧɨɜɨɝɨ ɲɟɜɟɪɚ α'

w 0

= arccos

cos σ

(4.34)

0 . sin β ' w 0

d

b0 ɉɪɢ β 0 = 0° , α ' w = arccos ′ . d 0 w0 ɍɝɨɥ ɧɚɤɥɨɧɚ ɡɭɛɶɟɜ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ

β'

w0

= arcsin

cos σ . cosα ' w0

(4.35)

Ɍɨɪɰɨɜɵɣ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ tgα '

w 0 . α ' = arctg tw cos β ' w

ɉɪɢ

β = 0°, 0

(4.36)

α' = α' . tw w 0 85

Ⱦɢɚɦɟɬɪ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟɫɚ d

d'

w

=

b . cos α' tw

(4.37)

Ⱦɥɢɧɚ ɥɢɧɢɢ ɡɚɰɟɩɥɟɧɢɹ ɩɪɢ ɲɟɜɢɧɝɨɜɚɧɢɢ ɧɨɜɵɦ ɲɟɜɟɪɨɦ (d ' L' = 0

(d ' )2 − d 2 )2 − d 2 w b w b 0 0 + . 2 ⋅ sin σ 2 ⋅ sin σ 0

(4.38)

ɇɚɢɛɨɥɶɲɢɣ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɩɪɨɮɢɥɹ ɡɭɛɚ ɲɟɜɟɪɚ ɫ ɭɱɟɬɨɦ ɩɟɪɟɤɪɵɬɢɹ ɨɛɪɚɛɨɬɤɨɣ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ ρ − ΔL ⎞ ⎛ p ⎟ ⋅ sin σ . ⎜ ρ ' = ⎜ L' − 0 ⎜ 0 0 sin σ ⎟⎟ ⎠ ⎝

(4.39)

ɉɪɨɜɟɪɢɬɶ ɜɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɹ: ρ' ≤ ρ , a 0 0

(4.40) ɝɞɟ ρ a0 = 0,5 ⋅ d a0 − d b0 . ȿɫɥɢ ɷɬɨ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɪɚɛɨɱɢɣ ɩɪɨɮɢɥɶ ɡɭɛɶɟɜ ɤɨɥɟɫɚ ɨɛɪɚ2

2

ɛɚɬɵɜɚɟɬɫɹ ɫ ɡɚɩɚɫɨɦ. ȿɫɥɢ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ, ɩɪɢɧɹɜ ρ a0 = ρ '0 , ɩɟɪɟɫɱɢɬɚɬɶ ɡɧɚɱɟɧɢɟ da0 : d

a

= 4ρ 2 + d 2 . a b 0 0 0

(4.4)

ɇɟɨɛɯɨɞɢɦɨ ɬɚɤɠɟ ɩɪɨɜɟɪɢɬɶ ɨɬɫɭɬɫɬɜɢɟ ɪɟɡɚɧɢɹ ɜɟɪɲɢɧɨɣ ɡɭɛɶɟɜ ɲɟɜɟɪɚ ɜɩɚɞɢɧɵ ɡɭɛɶɟɜ ɤɨɥɟɫɚ. Ⱦɨɥɠɧɨ ɛɵɬɶ ɜɵɞɟɪɠɚɧɨ ɭɫɥɨɜɢɟ: d'

w

+d '

w

−d 0

a

−d 0

f

≥ 0,2 m.

(4.42)

ɉɪɢ ɧɟɜɵɩɨɥɧɟɧɢɢ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɦɨɠɧɨ ɩɨɣɬɢ ɩɨ ɩɭɬɢ ɭɜɟɥɢɱɟɧɢɹ ɜɵh f (d f = d − 2h f ). ɫɨɬɵ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ Ⱦɥɹ ɷɬɨɝɨ, ɩɨɫɥɟ ɫɨɝɥɚɫɨɜɚɧɢɹ ɢɡɦɟɧɟɧɢɹ ɫ ɤɨɧɫɬɪɭɤɬɨɪɨɦ ɡɭɛɱɚɬɨɣ ɩɟɪɟɞɚɱɢ, ɫɥɟɞɭɟɬ ɩɪɨɢɡɜɟɫɬɢ ɢɡɦɟɧɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ. 86

ȼɨɡɦɨɠɧɵɦɢ ɩɭɬɹɦɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜ ɫɥɭɱɚɟ ɧɟɜɵɩɨɥɧɟɧɢɹ ɭɫɥɨɜɢɹ 4.40 ɦɨɝɭɬ ɛɵɬɶ ɭɦɟɧɶɲɟɧɢɟ ɩɪɢɩɭɫɤɚ ɧɚ ɩɟɪɟɬɨɱɤɭ Δ, ɚ ɬɚɤɠɟ ɢɡɦɟɧɟɧɢɹ ɜɟɥɢɱɢɧɵ ɩɪɢɩɭɫɤɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɫɯɨɞɧɨɝɨ ɩɪɨɮɢɥɹ ɡɭɛɚ ɲɟɜɟɪɚ Δ =a +a . (4.43) 2 ɉɪɢ ɤɚɠɞɨɣ ɩɨɩɵɬɤɟ ɭɦɟɧɶɲɟɧɢɹ ɚ1 ɧɚ ɜɟɥɢɱɢɧɭ 0,1ɚ1 ɫɥɟɞɭɟɬ ɭɜɟɥɢɱɢ-

ɜɚɬɶ ɚ2 ɧɚ ɬɭ ɠɟ ɜɟɥɢɱɢɧɭ. ɉɪɢ ɷɬɨɦ ɫɨɯɪɚɧɢɬɫɹ ɜɟɥɢɱɢɧɚ ɩɪɢɩɭɫɤɚ ɧɚ ɩɟɪɟɬɨɱɤɭ. ȼɨɡɦɨɠɧɵɦ ɩɭɬɟɦ ɦɨɠɟɬ ɛɵɬɶ ɢɡɦɟɧɟɧɢɟ ɱɢɫɥɚ ɡɭɛɶɟɜ ɲɟɜɟɪɚ z0 . ȿɫɥɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚɫɱɟɬɨɜ ɢɡɦɟɧɹɟɬɫɹ da0, ɬɨ ɫɥɟɞɭɟɬ ɩɪɨɢɡɜɟɫɬɢ ɩɟɪɟɪɚɫɱɟɬ ɪɚɡɦɟɪɚ ɪ (ɧɨ ɪ 0, ɦɦ), ɚ ɬɚɤɠɟ ɜɟɥɢɱɢɧ ha0, h0, Sn0. ɛ) ɫɬɨɱɟɧɧɵɦ ɲɟɜɟɪɨɦ ɇɚɱɚɥɶɧɵɣ ɞɢɚɦɟɬɪ ɫɬɨɱɟɧɧɨɝɨ ɲɟɜɟɪɚ

2a

2. (4.44) w0 tgα ɍɝɨɥ ɧɚɤɥɨɧɚ ɡɭɛɶɟɜ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɫɬɨɱɟɧɧɨɝɨ ɲɟɜɟɪɚ d ''

= d0 −

⎛ d ' 'w ⎞ ⎟ ⎜ 0 β '' = arctg ⎜ ⋅ tgβ ⎟. w 0 ⎜ d0 ⎟ 0 ⎝ ⎠

(4.45)

ɉɪɢ β 0 = 0° – β ' ' w0 = 0° ɍɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɫɬɨɱɟɧɧɨɝɨ ɲɟɜɟɪɚ α''

w 0

= arccos

cos σ

0 . sin β ' ' w 0

ɉɪɢ β 0 = 0° –

(4.46) d

α' '

w 0

= arccos

b 0 . d '' w 0

ɍɝɨɥ ɧɚɤɥɨɧɚ ɡɭɛɶɟɜ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ β ''

w

= arcsin

cos σ . cos α ' ' w 0

(4.47)

87

Ɍɨɪɰɨɜɵɣ ɭɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ tgα ' '

α''

tw

= arctg

w 0 . cos β ' ' w

(4.48)

ɉɪɢ β 0 = 0° – α ' 'tw = α ' ' w . 0 Ⱦɢɚɦɟɬɪ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟɫɚ d

d ''

w

=

b . cos α ' ' tw

(4.49)

Ⱦɥɢɧɚ ɥɢɧɢɢ ɡɚɰɟɩɥɟɧɢɹ ɩɪɢ ɲɟɜɢɧɝɨɜɚɧɢɢ ɤɨɥɟɫɚ ɫɬɨɱɟɧɧɵɦ ɲɟɜɟɪɨɦ (d ' ' L' ' = 0

(d ' ' )2 − d 2 )2 − d 2 w b w b 0 0 . + 2 sin σ 2 sin σ 0

(4.50)

ɇɚɢɛɨɥɶɲɢɣ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɩɪɨɮɢɥɹ ɡɭɛɚ ɲɟɜɟɪɚ ɫ ɭɱɟɬɨɦ ɩɟɪɟɤɪɵɬɢɹ ɨɛɪɚɛɨɬɤɨɣ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ ρ ⎛ p − ΔL ⎜ ρ ' ' = ⎜ L' ' − 0 ⎜ 0 sin σ ⎝

⎞ ⎟ ⋅ sin σ . ⎟⎟ 0 ⎠

(4.5)

ɇɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɫɬɨɱɟɧɧɨɝɨ ɲɟɜɟɪɚ 2 d // = 4⎛⎜ ρ // ⎞⎟ + d 2 . a b ⎝ 0⎠ 0 0

(4.52)

ɉɪɨɜɟɪɢɬɶ ɭɫɥɨɜɢɟ: d // + d // − d // − d ≥ 0.2 ⋅ m . w w a f 0 0

(4.53)

ȿɫɥɢ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɨɬɫɭɬɫɬɜɭɟɬ ɪɚɛɨɬɚ ɜɟɪɲɢɧɨɣ ɡɭɛɶɟɜ ɲɟɜɟɪɚ. ȿɫɥɢ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɫɥɟɞɭɟɬ ɭɦɟɧɶɲɢɬɶ ɜɟɥɢɱɢɧɭ ɩɪɢɩɭɫɤɚ ɚ ɧɚ ɩɟɪɟɬɨɱɤɭ. ɇɚɢɦɟɧɶɲɢɣ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɩɪɨɮɢɥɹ ɡɭɛɚ ɫɬɨɱɟɧɧɨɝɨ ɲɟɜɟɪɚ ɩɨ ɬɨɪɰɭ

ρ HM .0 = ρ 0// −

(L + ΔL )sin σ 0 sin σ

.

(4.54) 88

ɉɪɨɜɟɪɢɬɶ ɩɟɪɟɤɪɵɬɢɟ ɨɛɪɚɛɨɬɤɨɣ ɜɵɫɨɬɵ ɡɭɛɚ ɤɨɥɟɫɚ. Ⱦɥɹ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ ɞɢɚɦɟɬɪ ɨɤɪɭɠɧɨɫɬɢ ɜ ɬɨɱɤɟ ɧɚɱɚɥɚ ɡɚɰɟɩɥɟɧɢɹ ɫɬɨɱɟɧɧɨɝɨ ɲɟɜɟɪɚ: DH .Ɂ . = d b20 + (2 ρ HM .0 ) . 2

(4.55)

ɉɟɪɟɤɪɵɬɢɟ ɛɭɞɟɬ ɨɛɟɫɩɟɱɟɧɨ, ɟɫɥɢ Dɇ .Ɂ . > D f . ȿɫɥɢ ɷɬɨ ɭɫɥɨɜɢɟ ɧɟ ɜɵɞɟɪɠɢɜɚɟɬɫɹ, ɬɨ ɫɥɟɞɭɟɬ ɭɦɟɧɶɲɢɬɶ ɩɪɢɩɭɫɤ ɧɚ ɩɟɪɟɬɨɱɤɭ a2 ɧɚ 0, a2 . Ɂɚɬɟɦ ɩɟɪɟɫɱɢɬɚɬɶ ɩɚɪɚɦɟɬɪɵ ɫɪɟɞɧɟɦɨɞɭɥɶɧɨɝɨ ɲɟɜɟɪɚ ɡɚɧɨɜɨ.

(

)

Ɇɨɠɧɨ ɫɞɟɥɚɬɶ ɩɨɩɵɬɤɭ ɭɦɟɧɶɲɟɧɢɹ ɡɧɚɱɟɧɢɹ D f (ɧɨ D f ≥ d b 0 + 2 ). ɉɊɈȼȿɊɄȺ ɇȺ ȼɈɁɆɈɀɇɈɋɌɖ ɈȻɊȺȻɈɌɄɂ ɊȺȻɈɑȿɃ ɑȺɋɌɂ ɉɊɈɎɂɅə ɁɍȻȺ ɄɈɅȿɋȺ ɋ ɉɈɆɈɓɖɘ ɆȿɅɄɈɆɈȾɍɅɖɇɈȽɈ ɒȿȼȿɊȺ

Ⱦɥɢɧɚ ɥɢɧɢɢ ɡɚɰɟɩɥɟɧɢɹ ɩɪɢ ɲɟɜɢɧɝɨɜɚɧɢɢ ɤɨɥɟɫɚ L0 =

d2 − d b2 2 sin σ

+

d 02 − d b20 2 sin σ 0

.

(4.56)

ɇɚɢɛɨɥɶɲɢɣ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɩɪɨɮɢɥɹ ɡɭɛɚ ɲɟɜɟɪɚ ɫ ɭɱɟɬɨɦ ɩɟɪɟɤɪɵɬɢɹ ɨɛɪɚɛɨɬɤɨɣ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ ρ p − ΔL ⎞ ⎛ ⎟⎟ sin σ 0 . ρ 0 = ⎜⎜ L 0 − σ sin ⎝ ⎠

(4.57)

2 2 ȿɫɥɢ ρ 0 > 0,5 d a 0 − d b 0 , ɬɨ ɩɪɨɮɢɥɶ ɡɭɛɚ ɤɨɥɟɫɚ ɨɛɪɚɛɚɬɵɜɚɟɬɫɹ ɫ ɡɚ-

ɩɚɫɨɦ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɫɥɟɞɭɟɬ ɢɡɦɟɧɢɬɶ ɱɢɫɥɨ ɡɭɛɶɟɜ ɲɟɜɟɪɚ z0 ɢ ɩɨɜɬɨɪɢɬɶ ɪɚɫɱɟɬ ɡɚɧɨɜɨ. ɈɉɊȿȾȿɅȿɇɂȿ ɇȿȾɈɋɌȺɘɓɂɏ ɄɈɇɋɌɊɍɄɌɂȼɇɕɏ ɉȺɊȺɆȿɌɊɈȼ ȾɂɋɄɈȼɈȽɈ ɒȿȼȿɊȺ

Ɉɩɪɟɞɟɥɢɬɶ ɞɢɚɦɟɬɪ ɨɬɜɟɪɫɬɢɣ ɜ ɨɫɧɨɜɚɧɢɢ ɡɭɛɶɟɜ ɲɟɜɟɪɚ ɫ m > ,75ɦɦ ( d ɧɚ ɪɢɫ.4.). Ⱦɥɹ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ: - ɬɨɪɰɨɜɵɣ ɭɝɨɥ ɩɪɨɮɢɥɹ ɧɚ ɨɤɪɭɠɧɨɫɬɢ ɜɩɚɞɢɧ ɡɭɛɶɟɜ ɲɟɜɟɪɚ

89

d α

ft

= arccos 0

b 0 ; D f

(4.58)

- ɬɨɥɳɢɧɭ ɡɭɛɚ ɧɨɜɨɝɨ ɲɟɜɟɪɚ ɜ ɬɨɪɰɨɜɨɣ ɩɥɨɫɤɨɫɬɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ St 0 =

Sno ; cos β 0

(4.59)

- ɬɨɥɳɢɧɭ ɡɭɛɚ ɧɨɜɨɝɨ ɲɟɜɟɪɚ ɜ ɬɨɪɰɨɜɨɣ ɩɥɨɫɤɨɫɬɢ ɧɚ ɨɤɪɭɠɧɨɫɬɢ ɜɩɚɞɢɧ ⎛ St Sft 0 = D f ⎜⎜ 0 + invα ft 0 − invα ft 0 ⎝ d0

⎞ ⎟; ⎟ ⎠

(4.60)

- ɲɢɪɢɧɭ ɜɩɚɞɢɧ ɡɭɛɶɟɜ ɭ ɢɯ ɨɫɧɨɜɚɧɢɹ ɜ ɧɨɪɦɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ⎛ πD Tf = ⎜⎜ f − Sft 0 ⎝ z0

⎞ ⎟⎟ cos β 0 ; ⎠

(4.6)

- ɞɢɚɦɟɬɪ ɫɜɟɪɥɚ ɞɥɹ ɫɜɟɪɥɟɧɢɹ ɨɬɜɟɪɫɬɢɣ d = T f + 3 (ɨɤɪɭɝɥɢɬɶ ɞɨ 0, ɦɦ).

(4.62)

Ⱦɢɚɦɟɬɪ ɨɤɪɭɠɧɨɫɬɢ ɰɟɧɬɪɨɜ ɨɬɜɟɪɫɬɢɣ ɩɨɞ ɜɵɯɨɞ ɫɬɪɨɝɚɥɶɧɨɝɨ ɪɟɡɰɚ D ɰ = D f − d2 − Tf2 (ɨɤɪɭɝɥɢɬɶ ɞɨ 0, ɦɦ).

(4.63)

ɍɝɨɥ ɧɚɤɥɨɧɚ ɨɫɢ ɨɬɜɟɪɫɬɢɹ β (ɪɢɫ.4.): β = arctg

D f tgβ 0 . d0

(4.64)

Ⱦɥɹ ɲɟɜɟɪɨɜ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɯ ɞɥɹ ɲɟɜɢɧɝɨɜɚɧɢɹ ɫ ɪɚɞɢɚɥɶɧɨɣ ɩɨɞɚɱɟɣ, ɲɢɪɢɧɭ ɲɟɜɟɪɚ b0 ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɧɚɡɧɚɱɚɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ȽɈɋɌ 8570-80 ɢ ȽɈɋɌ 0222-8: m ≤ ,75 ɦɦ – b0 = 0 ÷ 5 ɦɦ; m ≥ ,75 ɦɦ – b0 = 20 ÷ 25 ɦɦ. ɂɫɩɨɥɧɟɧɢɟ ɤɚɧɚɜɨɤ (ɪɢɫ.4.) ɫɪɟɞɧɟɦɨɞɭɥɶɧɵɯ ɲɟɜɟɪɨɜ ɩɪɢɦɟɧɹɟɬɫɹ ɜ ɫɥɭɱɚɟ ɫɬɪɨɝɚɧɢɹ ɢɯ ɧɚ ɫɩɟɰɢɚɥɢɡɢɪɨɜɚɧɧɨɦ ɩɪɢɫɩɨɫɨɛɥɟɧɢɢ, 2 – ɧɚ ɫɩɟɰɢɚɥɢɡɢɪɨɜɚɧɧɨɦ ɫɬɚɧɤɟ ɩɨɥɭɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɩɪɢɧɰɢɩɚ ɞɟɣɫɬɜɢɹ, 3 - (ɨɞɧɚ

90

ɫɬɨɪɨɧɚ ɩɚɪɚɥɥɟɥɶɧɚ ɬɨɪɰɭ ɲɟɜɟɪɚ, ɞɪɭɝɚɹ - ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɧɚɩɪɚɜɥɟɧɢɸ ɡɭɛɚ) - ɧɚ ɫɩɟɰɢɚɥɢɡɢɪɨɜɚɧɧɨɦ ɫɬɚɧɤɟ. ɇɚ ɦɟɥɤɨɦɨɞɭɥɶɧɵɯ ɲɟɜɟɪɚɯ (m ≤ ,75 ɦɦ) ɤɚɧɚɜɤɢ ɩɪɨɬɚɱɢɜɚɸɬɫɹ ɱɟɪɟɡ ɜɟɫɶ ɡɭɛ (ɫɦ. ɪɢɫ.4.2) ɩɨ ɤɨɥɶɰɭ ɢɥɢ ɩɨ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ (ɜ ɜɢɞɟ ɪɟɡɶɛɵ).

Ɋɢɫ. 4.2. ɒɟɜɟɪ ɞɢɫɤɨɜɵɣ ɦɟɥɤɨɦɨɞɭɥɶɧɵɣ: ɚ) ɩɪɨɮɢɥɶ ɡɭɛɚ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ; ɛ) ɩɪɨɮɢɥɶ ɤɨɥɶɰɟɜɵɯ ɤɚɧɚɜɨɤ (ɬɚɛɥ. 4.4.) 9

Ɋɚɡɦɟɪɵ ɤɚɧɚɜɤɢ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚɫɱɟɬɚ, ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɩɪɢɛɥɢɡɢɬɟɥɶɧɵɟ. ɍɬɨɱɧɟɧɢɟ ɪɚɡɦɟɪɨɜ ɤɚɧɚɜɨɤ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɜɵɩɨɥɧɹɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ȽɈɋɌ 8570-80 ɢ ȽɈɋɌ 022-8 (ɬɚɛɥ.4. ɢ ɬɚɛɥ. 4.3, ɪɢɫ. 4.2 ɢ ɬɚɛɥ. 4.4). Ɍɚɛɥɢɰɚ 4.3 ɂɫɩɨɥɧɟɧɢɟ

ɂɫɩɨɥɧɟɧɢɟ 2

ɂɫɩɨɥɧɟɧɢɟ 3

Ⱦɟɥɢɬɟɥɶɧɵɣ ɞɢɚɦɟɬɪ d 0 , ɦɦ


80 250

Ɉɬ 2 ɞɨ 2,75 3 Ɉɬ 3 ɞɨ 5 ɋɜ. 5 ɞɨ 8

i 0,6 0,8 ,0 ,0

80

250

n 0

2

9

80

80 ɢ 250 l 0,6 0,8

t

S

h

ɧɟ 2,2

ɦɟɧɟɟ ,

7

250

n

9

,0 Ɍɚɛɥɢɰɚ 4.4

Ɇɨɞɭɥɶ m, ɦɦ Ɉɬ 0,2 ɞɨ 2,75 ɋɜ.0.28 ɞɨ 0,5 ɋɜ. 0,5 ɞɨ 0,7 0,8 0,9 ,0 ɋɜ. ɞɨ ,25 ɋɜ. ,25 ɞɨ ,75

t ,4 ,7 2,

l ,0 ,5 2,0 2,5

b 0,7 0,6 0,7 0,6

3,0 4,5

2,7

5

0,8

ɑɢɫɥɨ ɤɚɧɚɜɨɤ Ʉ 6 5 6

5

Ɍɨɥɳɢɧɚ ɡɭɛɚ ɧɨɜɨɝɨ ɲɟɜɟɪɚ ɩɨ ɯɨɪɞɟ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ

S x = d 0 ⋅ sin

Sno (ɡɧɚɱɟɧɢɟ sin ɭɝɥɚ ɜ ɪɚɞɢɚɧɧɨɣ ɦɟɪɟ). d0

(4.66)

ȼɵɫɨɬɚ ɝɨɥɨɜɤɢ ɡɭɛɚ ɧɨɜɨɝɨ ɲɟɜɟɪɚ ɞɨ ɯɨɪɞɵ hx =

d ao d 0 S − cos no . 2 2 d0

(4.67)

92

Ɂɧɚɱɟɧɢɹ Sx ɢ hx ɩɪɨɫɬɚɜɥɹɸɬɫɹ ɧɚ ɱɟɪɬɟɠɟ ɫ ɰɟɥɶɸ ɜɵɩɨɥɧɟɧɢɹ ɤɨɧɬɪɨɥɹ ɫ ɩɨɦɨɳɶɸ ɲɬɚɧɝɟɧɡɭɛɨɦɟɪɚ. 4.2. Ⱦɨɩɨɥɧɢɬɟɥɶɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɪɚɡɪɚɛɨɬɤɢ ɪɚɛɨɱɟɝɨ ɱɟɪɬɟɠɚ ɞɢɫɤɨɜɨɝɨ ɲɟɜɟɪɚ Ɋɚɛɨɱɢɣ ɱɟɪɬɟɠ ɞɢɫɤɨɜɨɝɨ ɲɟɜɟɪɚ ɜɵɩɨɥɧɹɟɬɫɹ ɜ ɦɚɫɲɬɚɛɟ :; ɜɫɟ ɜɢɞɵ, ɪɚɡɪɟɡɵ ɢ ɫɟɱɟɧɢɹ ɦɨɠɧɨ ɜɵɩɨɥɧɹɬɶ ɜ ɛɨɥɶɲɟɦ ɦɚɫɲɬɚɛɟ. ȼ ɲɬɚɦɩɟ ɜ ɝɪɚɮɟ «Ɇɚɬɟɪɢɚɥ» ɭɤɚɡɵɜɚɟɬɫɹ: ɋɬɚɥɶ Ɋ6Ɇ5 ȽɈɋɌ 9265-73 (ɦɨɠɧɨ ɩɪɢɦɟɧɹɬɶ ɦɚɪɤɢ ɛɵɫɬɪɨɪɟɠɭɳɟɣ ɫɬɚɥɢ ɩɨɜɵɲɟɧɧɨɣ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ Ɋ9Ʉ5, Ɋ9Ʉ0, Ɋ6Ɇ5Ʉ5). ɇɚɞ ɲɬɚɦɩɨɦ ɞɨɥɠɧɵ ɛɵɬɶ ɭɤɚɡɚɧɵ ɬɟɯɧɢɱɟɫɤɢɟ ɬɪɟɛɨɜɚɧɢɹ. ȼ ɜɟɪɯɧɟɦ ɩɪɚɜɨɦ ɭɝɥɭ ɭɤɚɡɵɜɚɟɬɫɹ ɲɟɪɨɯɨɜɚɬɨɫɬɶ Ra 2,5 ɜɫɟɯ ɨɫɬɚɥɶɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɲɟɜɟɪɚ, ɤɪɨɦɟ ɬɟɯ, ɧɚ ɤɨɬɨɪɵɯ ɧɚ ɱɟɪɬɟɠɟ ɞɨɥɠɧɚ ɛɵɬɶ ɩɪɨɫɬɚɜɥɟɧɚ ɲɟɪɨɯɨɜɚɬɨɫɬɶ ɜ ɦɢɤɪɨɦɟɬɪɚɯ: - ɛɨɤɨɜɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɡɭɛɶɟɜ

Ra 0,4;

- ɨɩɨɪɧɨɣ ɬɨɪɰɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ

Ra 0,4;

- ɩɨɜɟɪɯɧɨɫɬɢ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ: - ɤɥɚɫɫɚ ɬɨɱɧɨɫɬɢ ȺȺ, Ⱥ

Ra 0,25;

- ɤɥɚɫɫɚ ȼ

Ra 0,32;

- ɧɚɪɭɠɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ (ɜɟɪɲɢɧ ɡɭɛɶɟɜ): - ɤɥɚɫɫɚ ȺȺ

Ra 0,63;

- ɤɥɚɫɫɚ Ⱥ ɢ ȼ

Ra ,25.

Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ɲɟɜɟɪɚ ɡɚɜɢɫɢɬ ɨɬ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ ɤɨɥɟɫɚ: ɤɥ. ȺȺ – ɞɥɹ ɤɨɥɟɫ 5-ɣ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ; ɤɥ. Ⱥ – 6-ɣ; ɤɥ. ȼ – 7-ɣ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ. ɉɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɪɚɡɦɟɪɨɜ ɲɟɜɟɪɚ ɧɚ ɞɨɥɠɧɵ ɛɵɬɶ ɛɨɥɟɟ: - ɲɢɪɢɧɵ

j s 6;

- ɲɢɪɢɧɵ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ

ɋ ;

- ɪɚɡɦɟɪɚ ɞɨ ɞɧɚ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ

ɇ ;

93

- ɪɚɞɢɭɫɚ R 0,9

+ 0,3;

- ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ d ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 4.5. Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ Ⱥ

Ɍɚɛɥɢɰɚ 4.5. ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɦ + 0,003 + 0,005

- ɞɢɚɦɟɬɪɚ ɨɤɪɭɠɧɨɫɬɢ ɜɟɪɲɢɧ ɡɭɛɶɟɜ d a 0 ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 4.6. Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ Ⱥ ȼ - ɜɵɫɨɬɵ ɝɨɥɨɜɤɢ ɡɭɛɚ

Ɍɚɛɥɢɰɚ 4.6. ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɦ ± 0,02 ± 0,04 ± 0,04

ha 0 ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 4.7.

Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ Ⱥ ȼ

Ɍɚɛɥɢɰɚ 4.7. ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɜ ɦɦ m > 3,5 ɦɦ m = 0,5 ÷ 3,5 ± 0,02 ± 0,02 ± 0,05 ± 0,025 ± 0,05 ± 0,025

ɇɚ ɪɚɛɨɱɟɦ ɱɟɪɬɟɠɟ ɩɪɢ ɩɨɦɨɳɢ ɭɫɥɨɜɧɵɯ ɨɛɨɡɧɚɱɟɧɢɣ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ȽɈɋɌ 2.308-79 ɞɨɥɠɧɵ ɛɵɬɶ ɭɤɚɡɚɧɵ: - ɨɬɤɥɨɧɟɧɢɟ ɨɬ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɫɬɢ ɬɨɪɰɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 4.8. Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ Ⱥ ȼ

Ɍɚɛɥɢɰɚ 4.8. ɇɟɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɫɬɶ ɜ ɦɦ 0,005 0,007 0,008

- ɨɬɤɥɨɧɟɧɢɟ ɨɬ ɩɚɪɚɥɥɟɥɶɧɨɫɬɢ ɬɨɪɰɨɜɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 4.9.

94

Ɍɚɛɥɢɰɚ 4.9. ɇɟɩɚɪɚɥɥɟɥɶɧɨɫɬɶ ɜ ɦɦ 0,005 0,008 0,00


- ɪɚɞɢɚɥɶɧɨɟ ɛɢɟɧɢɟ ɡɭɛɱɚɬɨɝɨ ɜɟɧɰɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ. 4.0. Ɍɚɛɥɢɰɚ 4.0. Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ Ⱥ ȼ

Ȼɢɟɧɢɟ ɜ ɦɦ Ɇɨɞɭɥɶ m, ɦɦ Ɉɬ 0,5 ɞɨ 3,55 0,006 0,0 0,08

ɋɜ. 3,55 0,008 0,0 0,08

ȼ ɬɟɯɧɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɹɯ ɞɨɥɠɧɨ ɛɵɬɶ ɭɤɚɡɚɧɨ . ɇRCɷ 63...66. 2. ɇɚ ɜɫɟɯ ɩɨɜɟɪɯɧɨɫɬɹɯ ɲɟɜɟɪɚ ɧɟ ɞɨɥɠɧɨ ɛɵɬɶ ɬɪɟɳɢɧ, ɡɚɛɨɢɧ, ɜɵɤɪɨɲɟɧɧɵɯ ɦɟɫɬ, ɡɚɭɫɟɧɰɟɜ ɢ ɫɥɟɞɨɜ ɤɨɪɪɨɡɢɢ. 3. ɉɨɝɪɟɲɧɨɫɬɶ ɧɚɩɪɚɜɥɟɧɢɹ ɡɭɛɚ ≤ (ɬɚɛɥ. 4.)

Ɍɚɛɥɢɰɚ 4.. Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ Ⱥ ȼ

ɉɨɝɪɟɲɧɨɫɬɶ ɜ ɦɦ Ⱦɥɹ ɦɨɞɭɥɟɣ m, ɦɦ Ɉɬ 0,5 ɞɨ 3,55 ɋɜɵɲɟ 3,55 ± 0,006 ± 0,008 ± 0,009 ± 0,009 ± 0,0 ± 0,0

4. Ɉɬɤɥɨɧɟɧɢɟ ɨɬ ɷɤɜɢɞɢɫɬɚɬɧɨɫɬɢ ɧɚɩɪɚɜɥɟɧɢɣ ɫɬɨɪɨɧ ɨɞɧɨɝɨ ɡɭɛɚ ≤ (ɬɚɛɥ.4.2)

Ɍɚɛɥɢɰɚ 4.2. ɉɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɜ ɦɦ Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ Ⱦɥɹ ɦɨɞɭɥɟɣ m, ɦɦ Ɉɬ 0,5 ɞɨ 3,55 ɋɜɵɲɟ 3,55 ȺȺ 0,006 0,008 Ⱥ 0,009 0,009 ȼ 5. ɉɨɝɪɟɲɧɨɫɬɶ ɩɪɨɮɢɥɹ ɡɭɛɚ ≤ (ɬɚɛɥ. 4.3)

95


Ɍɚɛɥɢɰɚ 4.3. ɉɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɜ ɦɦ Ⱦɥɹ ɦɨɞɭɥɟɣ m, ɦɦ Ɉɬ 0,5 ɞɨ 3,55 ɋɜɵɲɟ 3,55 0,003 0,004 0,004 0,006 0,006 0,008

6.Ɋɚɡɧɨɫɬɶ ɨɤɪɭɠɧɵɯ ɲɚɝɨɜ ≤ (ɬɚɛɥ. 4.4) Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ Ⱥ ȼ

Ɍɚɛɥɢɰɚ 4.4. ɉɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɜ ɦɦ Ⱦɥɹ ɦɨɞɭɥɟɣ m, ɦɦ Ɉɬ 0,5 ɞɨ 3,55 ɋɜɵɲɟ 3,55 0,003 0,003 0,003 0,003 0,005 0,005

7. ɇɚɤɨɩɥɟɧɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɨɤɪɭɠɧɨɝɨ ɲɚɝɚ ≤ (ɬɚɛɥ. 4.5) Ʉɥɚɫɫ ɬɨɱɧɨɫɬɢ ȺȺ Ⱥ ȼ

Ɍɚɛɥɢɰɚ 4.5. ɉɨɝɪɟɲɧɨɫɬɶ ɜ ɦɦ Ⱦɥɹ ɦɨɞɭɥɟɣ m, ɦɦ Ɉɬ 0,5 ɞɨ 3,55 ɋɜɵɲɟ 3,55 0,006 0,0 0,02 0,02 0,06 0,06

8. Ɉɬɤɥɨɧɟɧɢɟ ɨɬ ɰɢɥɢɧɞɪɢɱɧɨɫɬɢ ɢ ɤɪɭɝɥɨɫɬɢ ɨɬɜ. ∅ (d) ≤ (ɬɚɛɥ. 4.6) Ɍɚɛɥɢɰɚ 4.6. ɉɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɜ ɦɦ 0,003 0,003 0,004


9. Ⱦɨɩɭɫɤɚɸɬɫɹ ɡɚɜɚɥɵ ɤɪɚɟɜ ɧɚ ɤɚɠɞɨɣ ɢɡ ɫɬɨɪɨɧ ɨɬɜ. ∅(d) ɞɥɢɧɨɣ ≤ (0,25 ɨɬ ɨɛɳɟɣ ɞɥɢɧɵ ɨɬɜɟɪɫɬɢɹ). Ⱦɨɩɭɫɤɚɟɬɫɹ ɪɚɡɛɢɜɚɧɢɟ ∅ (d) ɭ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ ɧɚ ɰɟɧɬɪɚɥɶɧɨɦ ɭɝɥɟ ɞɨ 20 $ . 0. Ɋɚɡɦɟɪɵ ɛɟɡ ɞɨɩɭɫɤɨɜ ɜɵɩɨɥɧɹɬɶ: ɨɯɜɚɬɵɜɚɟɦɵɯ ɩɨ ɇ2, ɨɯɜɚɬɵɜɚɸɳɢɯ ɩɨ h2, ɩɪɨɱɢɯ ± (IT4)/2. . Ɇɚɪɤɢɪɨɜɚɬɶ: m, α , β 0 , ɥɟɜ.(ɦɚɪɤɢɪɭɟɬɫɹ ɬɨɥɶɤɨ ɥɟɜɨɟ ɧɚɩɪɚɜɥɟɧɢɟ), ɤɥ. ȺȺ (ɢɥɢ Ⱥ,ȼ), Ɋ6Ɇ5, ɝɨɞ ɜɵɩɭɫɤɚ (ɩɪɢɜɨɞɹɬɫɹ ɤɨɧɤɪɟɬɧɵɟ ɫɜɟɞɟɧɢɹ ɩɨ ɜɫɟɦ ɩɚɪɚɦɟɬɪɚɦ). 96

5. ɊȺɋɑȿɌ ɂ ɉɊɈȿɄɌɂɊɈȼȺɇɂȿ ɑȿɊȼəɑɇɕɏ ɎɊȿɁ ȾɅə ɒɅɂɐȿȼɕɏ ȼȺɅɈȼ ɋ ɉɊəɆɈȻɈɑɇɕɆ ɉɊɈɎɂɅȿɆ ɁɍȻɖȿȼ 5.1. ɉɪɨɮɢɥɢɪɨɜɚɧɢɟ ɡɭɛɶɟɜ ɮɪɟɡɵ Ⱦɢɚɦɟɬɪ ɢ ɪɚɞɢɭɫ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ d w = D p2 − 0,75b p2 ; rw = 0,5d w .

(5.)

ɍɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɜɚɥɚ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ (ɪɢɫ.5.) ⎛b ⎞ γ w = arcsin⎜ p ⎟ . ⎝ dw ⎠

(5.2)

ɉɨɥɨɜɢɧɚ ɲɢɪɢɧɵ ɡɭɛɚ a=

bp

2 .

(5.3)

Ɋɢɫ 5.. Ƚɪɚɮɢɱɟɫɤɚɹ ɫɯɟɦɚ ɤ ɨɛɤɚɬɭ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ ɢ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ.

97

ȼɵɫɨɬɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɨɬ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ɞɨ ɜɟɪɲɢɧɵ hao : ɚ) ɞɥɹ ɮɪɟɡ ɛɟɡ ɭɫɢɤɨɜ

hao =

dw − d p 2

;

(5.4)

ɛ) ɞɥɹ ɮɪɟɡ ɫ ɭɫɢɤɚɦɢ ɪɚɫɱɟɬ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɫɥɟɞɭɸɳɢɦ ɮɨɪɦɭɥɚɦ: - ɭɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɫ ɭɫɢɤɨɦ ɩɪɢ ɜɟɪɲɢɧɟ

(0,5d )

2

α ɭɫ = arccos

p

− a2 ;

rw

(5.5)

- ɜɵɫɨɬɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɨɬ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ɞɨ ɜɟɪɲɢɧɵ ɭɫɢɤɚ

hao = rw ⋅ sin α ɭɫ (sin α ɭɫ − sin γ w ) .

(5.6)

Ɇɚɤɫɢɦɚɥɶɧɵɟ ɭɝɥɵ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ: ɚ) ɞɥɹ ɮɪɟɡ ɛɟɡ ɭɫɢɤɚ α max = α n.ɤ .

2 ⎡ sin γ h ⎤ sin γ w ⎞ ⎛ w = arcsin ⎢ + ⎜ ⎟ + ao ⎥ ; rw ⎥ ⎢ 2 ⎝ 2 ⎠ ⎦ ⎣

(5.7)

ɛ) ɞɥɹ ɮɪɟɡ ɫ ɭɫɢɤɨɦ

α max = α ɭɫ = arccos

⎛ dp ⎜⎜ ⎝ 2

2

⎞ ⎟⎟ − a 2 ⎠ . rw

(5.8)

ɍɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ɞɥɹ ɮɪɟɡ ɫ ɭɫɢɤɚɦɢ ɢ ɛɟɡ ɭɫɢɤɨɜ (ɪɢɫ.5.)

αw = γw .

(5.9)

Ⱦɥɹ ɪɚɫɱɟɬɚ ɤɨɨɪɞɢɧɚɬ ɬɨɱɟɤ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɫɥɟɞɭɟɬ ɡɚɞɚɬɶɫɹ ɪɹɞɨɦ ɡɧɚɱɟɧɢɣ ɤɨɨɪɞɢɧɚɬ Y ɡɭɛɚ ɮɪɟɡɵ (ɨɬ Y = 0 ɞɨ Ymax = ha0); ɡɚɬɟɦ ɩɨ ɮɨɪɦɭɥɟ 2 ⎡ sin γ yN ⎤ ⎛ sin γ w ⎞ w ⎢ ⎥, + ⎜ α N = arcsin ⎟ + r 2 2 ⎢ ⎠ ⎝ w ⎥ ⎣ ⎦

98

(5.0)

ɝɞɟ N - ɧɨɦɟɪ ɬɨɱɤɢ, ɨɩɪɟɞɟɥɢɬɶ ɭɝɥɵ ɩɪɨɮɢɥɹ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɬɨɱɤɚɯ. ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɚɛɫɰɢɫɫɵ ɏ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:

X N = rw (α N − γ w ) − (rw ⋅ sin α N − a ) ⋅ cos α N .

(5.)

Ɂɧɚɱɟɧɢɹ ɭɝɥɨɜ ɜ ɮɨɪɦɭɥɟ 5. ɜ ɪɚɞɢɚɧɚɯ. ȿɫɥɢ ((D – d) / d w ) ≤ 0,12, ɬɨ ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɩɪɨɮɢɥɶ ɡɭɛɚ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɡɚɦɟɧɹɟɬɫɹ ɞɭɝɨɣ ɨɞɧɨɣ ɨɤɪɭɠɧɨɫɬɢ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɡɚɦɟɧɚ ɞɭɝɚɦɢ ɞɜɭɯ ɨɤɪɭɠɧɨɫɬɟɣ, ɥɢɛɨ, ɱɬɨ ɰɟɥɟɫɨɨɛɪɚɡɧɟɟ, ɞɭɝɨɣ ɨɞɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɫ ɨɩɬɢɦɚɥɶɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɩɚɪɚɦɟɬɪɨɜ ɨɤɪɭɠɧɨɫɬɢ. ɉɨɫɥɟɞɧɟɟ ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɨ ɬɨɥɶɤɨ ɫ ɩɨɦɨɳɶɸ ɗȼɆ [9]. Ɂɚɦɟɧɚ ɤɪɢɜɨɣ ɩɪɨɮɢɥɹ ɞɭɝɨɣ ɨɞɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɦɨɠɟɬ ɛɵɬɶ ɨɫɭɳɟɫɬɜɥɟɧɚ ɪɚɫɱɟɬɨɦ ɩɨ ɫɥɟɞɭɸɳɟɣ ɦɟɬɨɞɢɤɟ. - Ⱦɢɚɦɟɬɪɵ ɩɪɨɮɢɥɶɧɵɯ ɬɨɱɟɤ ɡɭɛɚ ɜɚɥɚ

d = d w − hao ; d 2 = d w − ,8hao .

(5.2)

- ɉɪɨɮɢɥɶɧɵɟ ɭɝɥɵ ɡɭɛɚ ɜɚɥɚ γ = arcsin

bp d

; γ 2 = arcsin

bp d2

.

(5.3)

- ɉɪɨɮɢɥɶɧɵɟ ɭɝɥɵ ɜ ɫɨɩɪɹɠɟɧɧɵɯ ɬɨɱɤɚɯ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ

α = arccos -

d ⋅ cos γ d ⋅ cos γ 2 2 ; α 2 = arccos . d dw w

(5.4)

Ⱥɛɫɰɢɫɫɵ ɬɨɱɟɤ ɢ 2 ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ X = rw ( α − γ w ) – ( rw ⋅ sin α – a) cos α ;

X 2 = rw (α 2 − γ w ) − (rw ⋅ sin α 2 − a )cos α 2 .

(5.5)

- Ɉɪɞɢɧɚɬɵ ɬɨɱɟɤ ɢ 2 ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ Y = rw ⋅ sin 2 α − a ⋅ sin α ; Y2 = rw ⋅ sin 2 α 2 − a ⋅ sin α 2 .

(5.6)

ɍɝɥɵ ɜ ɮɨɪɦɭɥɚɯ ɩɨɞɫɱɟɬɚ ɤɨɨɪɞɢɧɚɬ ɜ ɪɚɞɢɚɧɚɯ. - Ⱥɛɫɰɢɫɫɚ ɰɟɧɬɪɚ ɡɚɦɟɧɹɸɳɟɣ ɨɤɪɭɠɧɨɫɬɢ (ɪɢɫ..3)

99

X0

(x =

2 2

)

(

)

+ y 22 ⋅ y − x2 + y2 ⋅ y 2 . 2(x2 ⋅ y − x ⋅ y 2 )

(5.7)

- Ɉɪɞɢɧɚɬɚ ɰɟɧɬɪɚ ɡɚɦɟɧɹɸɳɟɣ ɨɤɪɭɠɧɨɫɬɢ Y0

(x =

2 2

)

(

)

+ y22 ⋅ x − x2 + y2 ⋅ x2 . 2(x2 ⋅ y − x ⋅ y2 )

(5.8)

- Ɋɚɞɢɭɫ ɡɚɦɟɧɹɸɳɟɣ ɨɤɪɭɠɧɨɫɬɢ

R = X 02 + Y02 .

(5.9)

Ɉɩɪɟɞɟɥɟɧɢɟ ɩɨɝɪɟɲɧɨɫɬɟɣ ɩɪɢ ɡɚɦɟɧɟ ɤɪɢɜɨɣ ɩɪɨɮɢɥɹ ɞɭɝɨɣ ɨɞɧɨɣ ɨɤɪɭɠɧɨɫɬɢ [4]. A=

rw ⋅ γ w + x 0 ; y0 ⎞ ⎛ 2⎜ rw + ⎟ 3 ⎠ ⎝

B=

α m = A + A 2 + B ;

y0 y rw + 0 3

;

αm2 = A − A2 + B .

(5.20)

ȼɟɥɢɱɢɧɵ X 0 , Y0 ɩɨɞɫɬɚɜɥɹɸɬɫɹ ɜ ɮɨɪɦɭɥɵ ɫ ɭɱɟɬɨɦ ɡɧɚɤɨɜ. ɍɝɥɵ

α m ɢ α m 2 ɩɨɥɭɱɚɸɬɫɹ ɜ ɪɚɞɢɚɧɚɯ. Ⱥɛɫɰɢɫɫɵ ɢ ɨɪɞɢɧɚɬɵ ɩɪɨɮɢɥɶɧɵɯ ɬɨɱɟɤ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɧɚɢɛɨɥɶɲɢɦ ɨɬɤɥɨɧɟɧɢɹɦ, ɪɚɜɧɵ:

( = rw (α m

) ( − γ w ) − (rw ⋅ sin α m

) − a )cos α m

X m = rw α m − γ w − rw ⋅ sin α m − a cos α m Xm2

2

2

y m = rw ⋅ sin 2 α m − a ⋅ sin α m ;

2

; (5.2)

y m 2 = rw ⋅ sin 2 α m 2 − a ⋅ sin α m 2 . - Ɉɩɪɟɞɟɥɹɸɬɫɹ ɧɚɢɛɨɥɶɲɢɟ ɨɬɤɥɨɧɟɧɢɹ Δρ1 ɢ Δρ2 ɬɨɱɟɤ ɡɚɦɟɧɹɸɳɟɣ ɨɤɪɭɠɧɨɫɬɢ ɨɬ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɤɪɢɜɨɣ: Δρ =

(X

m

− X0

) + (Y

m

− Y0

)

− R ;

Δρ 2 =

(X

m2

− X0

) + (Y

m2

− Y0

)

− R .

2

2

2

2

- Ⱦɨɥɠɧɨ ɛɵɬɶ ɜɵɩɨɥɧɟɧɨ ɭɫɥɨɜɢɟ:

00

(5.22)

(ρ

+ ρ 2 ) ≤ 2 3 T .

(5.23)

ȿɫɥɢ ɷɬɨ ɭɫɥɨɜɢɟ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɩɪɨɢɡɜɨɞɢɬɫɹ ɡɚɦɟɧɚ ɞɭɝɚɦɢ ɞɜɭɯ ɨɤɪɭɠɧɨɫɬɟɣ (ɪɢɫ.5.2). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɢɚɦɟɬɪɵ ɨɤɪɭɠɧɨɫɬɟɣ, ɧɚ ɤɨɬɨɪɵɯ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɫɩɨɥɨɠɟɧɢɟ ɬɨɱɟɤ ɢ 2 d = d w − 0,5hao ; d 2 = d w − hao .

(5.24)

Ɂɧɚɱɟɧɢɹ γ , γ 2 , α , α 2 , X , X 2 , Y , Y2 , X 0 , Y0 , R ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ 5.3 - 5.9.

Ɋɢɫ. 5.2. Ɂɚɦɟɧɚ ɤɪɢɜɨɣ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɩɪɨɮɢɥɹ ɡɭɛɚ ɞɭɝɚɦɢ ɞɜɭɯ ɨɤɪɭɠɧɨɫɬɟɣ

Ⱦɢɚɦɟɬɪ ɨɤɪɭɠɧɨɫɬɢ ɢ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɬɪɟɬɶɟɣ ɩɪɨɮɢɥɶɧɨɣ ɬɨɱɤɢ ɲɥɢɰɚ

bp γ = arcsin d 3 = d w − ,8hao ; 3 d

(5.25)

3

ɉɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɬɪɟɬɶɟɣ ɩɪɨɮɢɥɶɧɨɣ ɬɨɱɤɢ ɡɭɛɚ ɮɪɟɡɵ

0

α 3 = arccos

d 3 ⋅ cos γ 3 . dw

(5.26)

Ⱥɛɫɰɢɫɫɚ ɢ ɨɪɞɢɧɚɬɚ ɬɪɟɬɶɟɣ ɩɪɨɮɢɥɶɧɨɣ ɬɨɱɤɢ ɡɭɛɚ ɮɪɟɡɵ

X 3 = rw (α 3 − γ w ) − (rw ⋅ sin α 3 − a )cos α 3 ;

Y3 = rw ⋅ sin 2 α 3 − a ⋅ sin α 3 .

(5.27)

ȼɫɩɨɦɨɝɚɬɟɥɶɧɵɟ ɭɝɥɵ Å3 ɢ Ε 0 ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ: Ε 3 = arctg

Y3 − Y2 ; X3 − X 2

Ε 0 = arctg

Y2 − Y0 . X0 − X2

(5.28)

ɝɞɟ ɏ0 ɢY0– ɤɨɨɪɞɢɧɚɬɵ ɰɟɧɬɪɚ ɩɟɪɜɨɣ ɨɤɪɭɠɧɨɫɬɢ. Ɋɚɞɢɭɫ ɜɬɨɪɨɣ ɨɤɪɭɠɧɨɫɬɢ R2 =

X3 − X 2 . 2 ⋅ cos Ε 0 ⋅ cos(Ε 3 + Ε 0 )

(5.29)

Ʉɨɨɪɞɢɧɚɬɵ ɰɟɧɬɪɚ ɜɬɨɪɨɣ ɨɤɪɭɠɧɨɫɬɢ X 0/ = R 2 ⋅ cos Ε 0 + X 2 ; Y0/ = −(R 2 ⋅ sin Ε 0 − Y2 ).

(5.30)

ɉɨɝɪɟɲɧɨɫɬɢ ɨɬ ɡɚɦɟɧɵ ɤɪɢɜɨɣ ɨɤɪɭɠɧɨɫɬɢ ɜɵɱɢɫɥɹɸɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɞɥɹ ɩɟɪɜɨɣ ɢ ɜɬɨɪɨɣ ɨɤɪɭɠɧɨɫɬɢ. ɍ ɜɬɨɪɨɣ ɨɤɪɭɠɧɨɫɬɢ ɩɨɝɪɟɲɧɨɫɬɶ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɞɥɹ ɦɟɧɶɲɟɝɨ ɭɝɥɚ α m , ɬ.ɤ. ɛɨɥɶɲɟɟ ɡɧɚɱɟɧɢɟ ɟɝɨ ɥɟɠɢɬ ɡɚ ɩɪɟɞɟɥɚɦɢ ɩɪɨɮɢɥɹ. Ⱦɥɹ ɮɪɟɡ ɛɟɡ ɭɫɢɤɨɜ ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ, ɫ ɤɨɬɨɪɨɣ ɧɚɱɢɧɚɟɬɫɹ ɩɟɪɟɯɨɞɧɚɹ ɤɪɢɜɚɹ ɨɬ ɛɨɤɚ ɲɥɢɰɚ ɤ ɜɧɭɬɪɟɧɧɟɣ ɨɤɪɭɠɧɨɫɬɢ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ:

X n.ɤ . = (rw ⋅ sin α n.ɤ . − a )cos α n.ɤ.

(5.3)

ɝɞɟ α n.ɤ. ɫɦ. ɮɨɪɦɭɥɭ 5.7. 2

rn.ɤ. = 0,5d n.ɤ.

⎛ dp ⎞ = ⎜⎜ ⎟⎟ + X n2.ɤ. ; dn.k. = 2r n.k. ⎝ 2 ⎠

02

(5.32)

ɉɪɨɜɟɪɢɬɶ ɜɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɹ ɜɨɡɦɨɠɧɨɫɬɢ ɲɥɢɰɟɜɨɝɨ ɫɨɟɞɢɧɟɧɢɹ ɞɥɹ ɜɚɥɨɜ ɢɫɩɨɥɧɟɧɢɹ ɋ ɢ ȼ (ɪɢɫ. .2). Ⱦɥɹ ɜɚɥɚ ɢɫɩɨɥɧɟɧɢɹ ɋ ɞɨɥɠɧɨ ɛɵɬɶ ɜɵɞɟɪɠɚɧɨ ɭɫɥɨɜɢɟ: d n.ɤ. ≤ (d + 2C max ).

(5.33)

Ⱦɥɹ ɜɚɥɚ ɢɫɩɨɥɧɟɧɢɹ ȼ ɞɨɥɠɧɨ ɛɵɬɶ ɜɵɞɟɪɠɚɧɨ ɭɫɥɨɜɢɟ: d n.ɤ. < d .

(5.34)

ȿɫɥɢ ɷɬɢ ɭɫɥɨɜɢɹ ɧɟ ɜɵɞɟɪɠɢɜɚɸɬɫɹ, ɬɨ ɩɪɨɢɡɜɨɞɢɬɫɹ ɚɧɚɥɢɡ ɫ ɰɟɥɶɸ ɜɵɹɜɥɟɧɢɹ ɜɨɡɦɨɠɧɨɫɬɢ ɢɡɦɟɧɟɧɢɹ (ɭɦɟɧɶɲɟɧɢɹ) rw . ɂɥɢ ɩɪɢ ɢɡɝɨɬɨɜɥɟɧɢɢ ɜɚɥɨɜ ɢɫɩɨɥɧɟɧɢɹ «ɋ» ɭɜɟɥɢɱɢɬɶ ɮɚɫɤɭ ɧɚ ɜɬɭɥɤɟ, ɚ ɩɪɢ ɢɡɝɨɬɨɜɥɟɧɢɢ ɜɚɥɨɜ ɢɫɩɨɥɧɟɧɢɹ «ȼ» - ɭɜɟɥɢɱɢɬɶ ɞɢɚɦɟɬɪ ɜɚɥɚ d. Ⱥɥɝɨɪɢɬɦ ɡɚɦɟɧɵ ɤɪɢɜɨɣ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɞɭɝɨɣ ɨɤɪɭɠɧɨɫɬɢ ɫ ɨɩɬɢɦɚɥɶɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɩɚɪɚɦɟɬɪɨɜ: ɪɚɞɢɭɫɚ R ɢ ɤɨɨɪɞɢɧɚɬ ɰɟɧɬɪɚ ɨɤɪɭɠɧɨɫɬɢ ɏ0 ɢ Y0 - ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 5.3 [9]. ɒɚɝ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ Ɋn0 ɢ ɬɨɥɳɢɧɚ ɡɭɛɶɟɜ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ S n0 : pno =

πd w ⎛π ⎞ ɢ S no = d w ⎜ − γ w ⎟ , z ⎝z ⎠

(5.35)

ɝɞɟ γ w – ɜ ɪɚɞɢɚɧɚɯ.

5.2. Ɋɚɫɱɟɬ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɞɥɹ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɫ ɩɪɹɦɨɛɨɱɧɵɦ ɩɪɨɮɢɥɟɦ

ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɨ ɡɧɚɱɟɧɢɟɦ Ɋ no ɢɡ ɬɚɛɥ. 5. ɜɵɛɪɚɬɶ ɡɧɚɱɟɧɢɹ ɫɥɟɞɭɸɳɢɯ ɩɚɪɚɦɟɬɪɨɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ: d ao – ɧɚɪɭɠɧɨɝɨ ɞɢɚɦɟɬɪɚ; d – ɞɢɚɦɟɬɪɚ ɛɭɪɬɢɤɨɜ; dɨɬɜ – ɞɢɚɦɟɬɪɚ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ; d ɜ - ɞɢɚɦɟɬɪɚ ɜɵɬɨɱɤɢ ɜ ɨɬɜɟɪɫɬɢɢ; Lmin - ɦɢɧɢɦɚɥɶɧɨɣ ɞɥɢɧɵ ɛɭɪɬɢɤɚ (ɫɦ. ɪɢɫ. .3).

03

Ɋɢɫ. 5.3. Ⱥɥɝɨɪɢɬɦ ɨɩɪɟɞɟɥɟɧɢɹ ɨɩɬɢɦɚɥɶɧɨɣ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɱɟɪɜɹɱɧɨ-ɲɥɢɰɟɜɨɣ ɮɪɟɡɵ ɞɭɝɨɣ ɨɤɪɭɠɧɨɫɬɢ 04

Ɍɚɛɥɢɰɚ 5.. ɒɚɝ ɩɨ ɧɨɪɦɚɥɢ Ɉɬ Ⱦɨ 0,5 3 3, 4 4, 6,5 6,6 9 9, , 3 3, 5 5, 6 6, 8,5 8,6 2 2, 25 25, 27 27, 30

d ao

d

d ɨɬɜ

d

ɜ

f

f2

l min

40 50 55 63 70 75 80 85 95 00 0 20 40

26 35 35 35 40 40 40 48 48 48 48 48 60

6 22 22 22 27 27 27 32 32 32 32 32 40

8 24 24 24 29 29 29 34 34 34 34 34 42

0,7 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,5

,0 ,5 ,5 ,5 ,5 ,5 ,5 2,0 2,0 2,0 2,0 2,0 2,0

2,5 2,5 2,5 3 3 3 3 3 3 3,5 3,5 3,5 3,5

ɑɢɫɥɨ ɡɭɛɶɟɜ ɮɪɟɡɵ

z0 ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ:

ɩɪɢ d ao ≤ 85 ɦɦ - z 0 = 2; ɩɪɢ d ao > 90 ɦɦ - z 0 = 4.

(5.36)

ɍɝɨɥ ɫɤɨɫɚ ɮɚɫɤɢ β 2 ɧɚɡɧɚɱɚɸɬ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɱɢɫɥɚ ɡɭɛɶɟɜ ɜɚɥɚ z. z =4 ÷ 8

- β 2 = 35 $ ;

z = 0 ÷ 4 - β 2 = 40 $ ;

(5.37)

z = 6 ÷ 20 - β 2 = 45 $ . ɋɤɨɫ ɮɚɫɤɢ ɨɬ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ Lc . ɚ) ɉɪɢ ɜɟɥɢɱɢɧɟ ɮɚɫɤɢ «ɋ» ɛɨɥɶɲɟ ɡɚɞɚɧɧɨɣ ɋmin ɪɚɫɱɟɬ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ:

γ B = arcsin

bp Dp

; α B = arccos

(

D p ⋅ cos γ B dw

)

L = 0,5D cos α − γ − 0,5d . c p B B w

05

;

(5.38)

ɛ) ɉɪɢ ɜɟɥɢɱɢɧɟ ɮɚɫɤɢ «ɋ» ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɞɚɧɧɨɣ ɜɟɥɢɱɢɧɨɣ ɋmin ɪɚɫɱɟɬ Lc ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ: γ Bf =

D p ⋅ cos γ B f bp π − arcsin ; ; α B f = arccos 4 Dp dw

(

)

L c = 0,5D p ⋅ cos α B f − γ B f − 0,5d w .

(5.39)

ȼɩɨɥɧɟ ɞɨɩɭɫɬɢɦ ɪɚɫɱɟɬ ɩɨ ɮɨɪɦɭɥɟ:

L/c =

Dp − d w 2

.

(5.40)

ɜ) ȿɫɥɢ d w =D p , ɬɨ L c =0.

(5.4)

ȼɵɫɨɬɚ ɮɚɫɤɢ h ɮ =ɋ max ,

(5.42)

ɝɞɟ ɋ max – ɦɚɤɫɢɦɚɥɶɧɚɹ ɜɟɥɢɱɢɧɚ ɮɚɫɤɢ ɧɚ ɲɥɢɰɟɜɨɦ ɜɚɥɭ. $ Ɂɚɞɧɢɣ ɭɝɨɥ ɩɪɢ ɜɟɪɲɢɧɟ ɡɭɛɚ ɮɪɟɡɵ α ɜ = 2 .

(5.43)

ɉɚɞɟɧɢɟ ɡɚɬɵɥɤɚ ɨɫɧɨɜɧɨɝɨ ɡɚɬɵɥɨɜɚɧɢɹ K=

πd

ao ⋅ tgα ɜ. z 0

(5.44)

Ɂɧɚɱɟɧɢɟ Ʉ ɨɤɪɭɝɥɢɬɶ ɞɨ ɛɥɢɠɚɣɲɟɝɨ ɡɧɚɱɟɧɢɹ ɫ ɤɪɚɬɧɨɫɬɶɸ ɚ 0 =0,5 ɦɦ. ɉɚɞɟɧɢɟ ɡɚɬɵɥɤɚ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɡɚɬɵɥɨɜɚɧɢɹ Ʉ = (,5 ÷ ,8)Ʉ. ȼɵɫɨɬɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ

h0 = hao + Lc + hɮ .

(5.45)

Ɋɚɡɦɟɪɵ ɤɚɧɚɜɤɢ ɞɥɹ ɨɛɥɟɝɱɟɧɢɹ ɲɥɢɮɨɜɚɧɢɹ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɜɵɱɢɫɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ: Ƚɥɭɛɢɧɚ ɤɚɧɚɜɤɢ ɩɪɢ ɭɫɥɨɜɢɢ ɟɟ ɡɚɬɵɥɨɜɚɧɢɹ hk = (0,5 ÷ )ɦɦ .

(5.46)

Ɍɨ ɠɟ – ɩɪɢ ɧɟɡɚɬɵɥɨɜɚɧɢɢ h k = (K + 0,5) ɦɦ.

(5.47)

ɒɢɪɢɧɚ ɤɚɧɚɜɤɢ 06

πD p

(

)(

)

− Sno −2 hɮ tgβ 2 −2 0,5d w α B −γ w − 0,5 d w ⋅sin α B −a cosα B L = z

).

(5.48)

ɋ ɞɨɫɬɚɬɨɱɧɨɣ ɬɨɱɧɨɫɬɶɸ L =

2hɮ πd w 2 Lc − S no − − . z tgβ 2 tgα B

(5.49)

Ɋɚɞɢɭɫ r 0 = ÷ 2 ɦɦ. ɉɪɢ ɧɚɥɢɱɢɢ ɛɭɪɬɢɤɚ (ɭɫɬɭɩɚ) ɧɚ ɲɥɢɰɟɜɨɦ ɜɚɥɭ, ɬ.ɟ. ɩɪɢ D ɭɫɬ > D, ɠɟɥɚɬɟɥɶɧɚ ɬɪɚɩɟɰɟɢɞɚɥɶɧɚɹ ɮɨɪɦɚ ɤɚɧɚɜɤɢ ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɲɢɪɢɧɵ ɤ ɞɧɭ ɤɚɧɚɜɤɢ, ɬ.ɟ. ɫ ɭɝɥɨɦ ɩɪɨɮɢɥɹ β k = 5 $ . ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɪɚɡɦɟɪɵ ɤɚɧɚɜɤɢ ɛɭɞɭɬ ɪɚɜɧɵ: L =

πD

p

z

−S

no

)(

(

)

)

− 2h tgβ − 2 0,5d α − γ − 0,5d ⋅ sin α − a cosα ; (5.50) ɮ w B B w B B 2

hk = K + (D ɭɫɬ − D p ) 2 + 0,5 ; r 0 = ɦɦ.

ɉɨɥɧɚɹ ɜɵɫɨɬɚ ɡɭɛɚ ɮɪɟɡɵ h = h0 + hk .

(5.5)

Ⱦɥɹ ɮɪɟɡ ɫ ɭɫɢɤɚɦɢ ɩɚɪɚɦɟɬɪɵ ɭɫɢɤɚ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɫɥɟɞɭɸɳɢɦ ɮɨɪɦɭɥɚɦ: - ɜɵɫɨɬɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɨɬ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ɞɨ ɭɫɢɤɚ h ɭɫ =

dw − dp 2

;

(5.52)

- ɲɢɪɢɧɚ ɭɫɢɤɚ b ɭɫ ɢ ɭɝɨɥ ɭɫɢɤɚ β ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɫɥɟɞɭɸɳɢɦ ɮɨɪɦɭɥɚɦ [5]: δ F = arcsin

aɰ dp

,

(5.53)

ɝɞɟ ɚ ɰ – ɪɚɡɦɟɪ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɱɚɫɬɢ ɦɟɠɞɭ ɡɭɛɶɹɦɢ (ɫɦ. ɪɢɫ..2). μ = arccos

XF =

(

)

−h w ao ; ϕ = μ + δ ; F d p

2 0 ,5 d

Sno − 0,5d w ⋅ϕ + 0,5d p ⋅ sin μ ; 2 07

bɭɫ = 0,5d w (α max − γ w ) − (0,5d w ⋅ sin α max − a )cos α max − X F ; β =

h ao π 80 ⋅ β − arctg ; β0 = . π 2 0,5d p ⋅ sin μ

ɉɟɪɟɞɧɢɣ ɭɝɨɥ γ = 0 $ .

(5.54) (5.55)

Ɇɢɧɢɦɚɥɶɧɵɣ ɡɚɞɧɢɣ ɭɝɨɥ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɛɨɤɨɜɨɣ ɪɟɠɭɳɟɣ ɤɪɨɦɤɟ

⎛ kz a ⎞ α δ = arctg⎜⎜ 0 ⋅ ⎟⎟ . ⎝ πd ao rw ⎠

(5.56)

Ⱦɨɥɠɧɨ ɛɵɬɶ α δ > $ . ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɩɨɩɵɬɤɭ ɭɦɟɧɶɲɟɧɢɹ r w . ɇɨ ɷɬɨ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɢɫɤɚɠɟɧɢɸ ɩɪɨɮɢɥɹ ɡɭɛɚ ɜɚɥɚ ɩɪɢ ɟɝɨ ɜɟɪɲɢɧɟ. Ƚɥɭɛɢɧɚ ɤɚɧɚɜɤɢ ɇ ɤ , ɪɚɞɢɭɫ ɡɚɤɪɭɝɥɟɧɢɹ ɜ ɨɫɧɨɜɚɧɢɢ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ r ɤ , ɭɝɨɥ ɩɪɨɮɢɥɹ ɤɚɧɚɜɤɢ Θ (ɪɢɫ..2): ɚ) ɞɥɹ ɮɪɟɡ ɫ ɡɚɬɵɥɨɜɚɧɧɵɦɢ ɤɚɧɚɜɤɚɦɢ Hɤ = h +

Ʉ + Ʉ + ; 2

(5.57)

ɛ) ɞɥɹ ɮɪɟɡ ɫ ɧɟɡɚɬɵɥɨɜɚɧɧɵɦɢ ɤɚɧɚɜɤɚɦɢ H Ʉ = h0 +

Ʉ + Ʉ + (K + 0,5) + . 2

(5.58)

Ɂɧɚɱɟɧɢɟ ɇ K ɨɤɪɭɝɥɹɟɬɫɹ ɜ ɛɨɥɶɲɭɸ ɫɬɨɪɨɧɭ ɫ ɤɪɚɬɧɨɫɬɶɸ ɚ 0 = 0,5 ɦɦ. r K = 1 ÷ 2 ɦɦ; Θ = 22 $ ; 25 $ ; 30 $ . Ȼɨɥɶɲɟɟ ɡɧɚɱɟɧɢɟ ɨɛɥɟɝɱɚɟɬ ɩɪɨɰɟɫɫ ɡɚɬɵɥɨɜɚɧɢɹ ɪɟɡɰɨɦ, ɭɜɟɥɢɱɢɜɚɟɬ ɨɛɴɟɦ ɩɪɨɫɬɪɚɧɫɬɜɚ ɞɥɹ ɪɚɡɦɟɳɟɧɢɹ ɫɬɪɭɠɤɢ. Ⱦɥɢɧɚ ɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɡɭɛɚ

ɋ=

πd ao . 3z 0

(5.59)

ɉɪɚɜɢɥɶɧɨɫɬɶ ɜɵɛɨɪɚ ɷɬɨɣ ɜɟɥɢɱɢɧɵ ɦɨɠɧɨ ɩɪɨɜɟɪɢɬɶ ɩɪɨɱɟɪɱɢɜɚɧɢɟɦ ɢɥɢ ɩɭɬɟɦ ɪɚɫɱɟɬɚ.

08

Ⱦɥɢɧɚ ɮɪɟɡɵ L ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ: L = 2 hao (D p − hao ) + (4 ÷ 0,5)Pno + 2 Lmin .

(5.60)

ɨɤɪɭɝɥɹɟɬɫɹ ɞɨ 0,5 ɢɥɢ ɰɟɥɨɝɨ ɱɢɫɥɚ. Ⱦɥɢɧɚ ɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ɩɪɢ

L = 22 ÷ 30

L ɲ = (0,25 ÷ 0,4) L;

L = 30 ÷ 90

L = (0,2 ÷ 0,3) L;

L > 90

L = (0,2 ÷ 0,25) L.

(5.6)

Ɋɚɡɦɟɪɵ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ ɢ ɞɨɩɭɫɤɢ ɧɚ ɧɢɯ ɧɚɡɧɚɱɚɸɬɫɹ ɩɨ ɬɚɛɥ.2.4. ɋɪɟɞɧɢɣ ɪɚɫɱɟɬɧɵɣ ɞɢɚɦɟɬɪ D t = d ao − 2h ao − 0,5K .

(5.62)

ɍɝɨɥ ɧɚɤɥɨɧɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ω t = arcsin

ω ⋅ 80 p no ; ωt $ = t . πD t π

(5.63)

Ⱦɨɥɠɧɨ ɛɵɬɶ ω t ≤ 7 $ . ɂɧɚɱɟ ɫɥɟɞɭɟɬ ɭɜɟɥɢɱɢɬɶ d ao . ɍɝɨɥ ɧɚɤɥɨɧɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ ωɤ = ω t .

(5.64)

Ɉɫɟɜɨɣ ɲɚɝ ɤɚɧɚɜɤɢ Pz =

πD t . tgωɤ

(5.65)

ɒɚɝ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɜɞɨɥɶ ɨɫɢ ɮɪɟɡɵ Pɨɫ.ɨ =

p no . cos ω t

(5.66)

5.3. ɋɩɪɚɜɨɱɧɚɹ ɢɧɮɨɪɦɚɰɢɹ ɞɥɹ ɪɚɡɪɚɛɨɬɤɢ ɪɚɛɨɱɟɝɨ ɱɟɪɬɟɠɚ ɱɟɪɜɹɱɧɨ-ɲɥɢɰɟɜɨɣ ɮɪɟɡɵ Ɋɚɛɨɱɢɣ ɱɟɪɬɟɠ ɱɟɪɜɹɱɧɨɣ ɲɥɢɰɟɜɨɣ ɮɪɟɡɵ ɜɵɩɨɥɧɹɟɬɫɹ ɜ ɦɚɫɲɬɚɛɟ :. ɋɟɱɟɧɢɟ ɩɥɨɫɤɨɫɬɶɸ, ɧɨɪɦɚɥɶɧɨɣ ɤ ɜɢɧɬɨɜɨɣ ɧɚɪɟɡɤɟ, ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɨ ɜ ɛɨɥɶɲɟɦ ɦɚɫɲɬɚɛɟ. 09

Ɏɪɟɡɵ ɢɡɝɨɬɚɜɥɢɜɚɸɬɫɹ ɢɡ ɛɵɫɬɪɨɪɟɠɭɳɢɯ ɫɬɚɥɟɣ Ɋ6Ɇ5, Ɋ6Ɇ5Ʉ5, Ɋ6ȺɆ5, Ɋ9Ʉ0, Ɋ4Ɏ4 ȽɈɋɌ 925-73 ɬɪɟɯ ɤɥɚɫɫɨɜ ɬɨɱɧɨɫɬɢ Ⱥ, ȼ, ɋ. ɉɪɢ ɷɬɨɦ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɦɟɧɹɬɶ ɮɪɟɡɵ ɤɥɚɫɫɚ ɬɨɱɧɨɫɬɢ Ⱥ ɞɥɹ ɱɢɫɬɨɜɨɝɨ ɧɚɪɟɡɚɧɢɹ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɫ ɞɨɩɭɫɤɨɦ ɧɚ ɬɨɥɳɢɧɭ ɡɭɛɚ ɩɨ 9 ɤɜɚɥɢɬɟɬɭ ɢ ɩɨ ɰɟɧɬɪɢɪɭɸɳɢɦ ɞɢɚɦɟɬɪɚɦ; ɜɧɭɬɪɟɧɧɟɦɭ ɩɨ - ɟ8 ɢ ɧɚɪɭɠɧɨɦɭ - ɩɨ ȽɈɋɌ 3980. Ɏɪɟɡɵ ɬɨɱɧɨɫɬɢ ȼ - ɞɥɹ ɱɢɫɬɨɜɨɝɨ ɧɚɪɟɡɚɧɢɹ ɜɚɥɨɜ ɫ ɞɨɩɭɫɤɨɦ ɧɚ ɬɨɥɳɢɧɭ ɡɭɛɚ ɩɨ 0 ɤɜɚɥɢɬɟɬɭ ɢ ɩɨ ɰɟɧɬɪɢɪɭɸɳɢɦ ɞɢɚɦɟɬɪɚɦ: ɜɧɭɬɪɟɧɧɟɦɭ - ɟ9 ɢ ɧɚɪɭɠɧɨɦɭ - ɩɨ ȽɈɋɌ 39-80. Ɏɪɟɡɵ ɬɨɱɧɨɫɬɢ ɋ - ɞɥɹ ɱɟɪɧɨɜɨɝɨ ɧɚɪɟɡɚɧɢɹ ɜɚɥɨɜ ɩɨɞ ɩɨɫɥɟɞɭɸɳɟɟ ɲɥɢɮɨɜɚɧɢɟ. ȼ ɜɟɪɯɧɟɦ ɩɪɚɜɨɦ ɭɝɥɭ ɱɟɪɬɟɠɚ ɭɤɚɡɵɜɚɟɬɫɹ ɲɟɪɨɯɨɜɚɬɨɫɬɶ Ra 2,5, ɤɪɨɦɟ ɬɟɯ ɩɨɜɟɪɯɧɨɫɬɟɣ, ɧɚ ɤɨɬɨɪɵɯ ɧɟ ɱɟɪɬɟɠɟ ɞɨɥɠɧɚ ɛɵɬɶ ɩɪɨɫɬɚɜɥɟɧɚ ɲɟɪɨɯɨɜɚɬɨɫɬɶ ɜ ɦɢɤɪɨɦɟɬɪɚɯ: ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ɮɪɟɡ ɤɥɚɫɫɨɜ ɬɨɱɧɨɫɬɢ: Ⱥ - 0,32; ȼ - 0,63; ɋ - 0,63; ,25; ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɞɥɹ ɮɪɟɡ ɤɥɚɫɫɨɜ ɬɨɱɧɨɫɬɢ: Ⱥ, ȼ - 0,63; ɋ - ,25; ɡɚɞɧɟɣ ɛɨɤɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɡɭɛɚ ɢ ɡɚɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨ ɜɟɪɲɢɧɟ ɡɭɛɚ ɞɥɹ ɮɪɟɡ ɤɥɚɫɫɨɜ ɬɨɱɧɨɫɬɢ: Ⱥ - 0,32; 0,63; ȼ - 0,63; ɋ - ,25; ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɛɭɪɬɢɤɨɜ ɞɥɹ ɮɪɟɡ ɤɥɚɫɫɨɜ ɬɨɱɧɨɫɬɢ: Ⱥ - 0,32; 0,63; ȼ - 0,63; ɋ - 0,63; ,25; ɬɨɪɰɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɛɭɪɬɢɤɨɜ ɞɥɹ ɮɪɟɡ ɤɥɚɫɫɨɜ ɬɨɱɧɨɫɬɢ: Ⱥ, ȼ - 0,63; ɋ - 0,63; ,25. ɉɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ

ɩɨ ɧɚɪɭɠɧɨɦɭ ɞɢɚɦɟɬɪɭ ɛɭɪɬɢɤɨɜ ɢ ɨɛɳɟɣ

ɞɥɢɧɟ – h 6. ɇɚ ɪɚɛɨɱɟɦ ɱɟɪɬɟɠɟ ɩɪɢ ɩɨɦɨɳɢ ɭɫɥɨɜɧɵɯ ɨɛɨɡɧɚɱɟɧɢɣ ɞɨɥɠɧɵ ɛɵɬɶ ɭɤɚɡɚɧɵ (ɬɚɛɥ.5.2) f y , f t , f

rd a

, f γ ; ɧɚ ɱɟɪɬɟɠɟ ɩɨɤɚɡɚɬɶ ɬɨɱɧɨɫɬɶ ɩɨɫɚɞɨɱɧɨ-

0

ɝɨ ɨɬɜɟɪɫɬɢɹ f

d,

ɨɫɟɜɨɝɨ ɲɚɝɚ ɡɭɛɶɟɜ f

px

, ɬɨɥɳɢɧɵ ɡɭɛɶɟɜ ɜ ɧɨɪɦɚɥɶɧɨɦ 0

ɫɟɱɟɧɢɢ Ɍ so . Ɇɟɫɬɨ ɦɚɪɤɢɪɨɜɤɢ – ɷɬɨ ɬɨɪɟɰ ɮɪɟɡɵ. ɇɚ ɱɟɪɬɟɠɟ ɢɧɫɬɪɭɦɟɧɬɚ ɞɨɥɠɧɨ ɛɵɬɶ ɭɤɚɡɚɧɨ ɦɟɫɬɨ ɦɚɪɤɢɪɨɜɤɢ ɫ ɭɤɚɡɚɧɢɟɦ ɩɭɧɤɬɚ ɬɟɯɧɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɣ. ȼ ɩɭɧɤɬɟ ɬɟɯɧɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɣ ɞɨɥɠɧɚ ɛɵɬɶ ɩɪɢɜɟɞɟɧɚ ɤɨɧɤɪɟɬɧɚɹ ɦɚɪɤɢɪɨɜɨɱɧɚɹ ɧɚɞɩɢɫɶ. ȼ ɬɟɯɧɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɹɯ ɞɨɥɠɧɨ ɛɵɬɶ ɭɤɚɡɚɧɨ: . ɇRC ɷ 63 ... 65∗. 2. ɇɚ ɜɫɟɯ ɩɨɜɟɪɯɧɨɫɬɹɯ ɧɟ ɞɨɥɠɧɨ ɛɵɬɶ ɬɪɟɳɢɧ, ɡɚɭɫɟɧɰɟɜ ɢ ɫɥɟɞɨɜ ɤɨɪɪɨɡɢɢ. 3. ɇɟɩɨɥɧɵɟ ɜɢɬɤɢ ɫɧɹɬɶ ɞɨ ɬɨɥɳɢɧɵ ɡɭɛɶɟɜ ɧɟ ɦɟɧɟɟ ɩɨɥɨɜɢɧɵ ɬɨɥɳɢɧɵ ɜɟɪɲɢɧ ɰɟɥɶɧɵɯ ɡɭɛɶɟɜ. 4. Ɉɬɤɥɨɧɟɧɢɟ ɲɚɝɚ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ∗∗ ≤ ... f uo . 5. ɇɚɤɨɩɥɟɧɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɨɤɪɭɠɧɨɝɨ ɲɚɝɚ ɤɚɧɚɜɨɤ ≤ ... F p . 0

6. Ɉɬɤɥɨɧɟɧɢɟ ɧɚɩɪɚɜɥɟɧɢɹ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ ≤ ... f x . 7. Ɉɬɤɥɨɧɟɧɢɟ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ≤ ... f f 0 . 8. Ɉɬɤɥɨɧɟɧɢɟ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɮɪɟɡɵ ɧɚ ɨɞɧɨɦ ɨɛɨɪɨɬɟ ≤ ... f no . 9. Ɉɬɤɥɨɧɟɧɢɟ ɨɫɟɜɨɝɨ ɲɚɝɚ ɧɚ ɜɟɥɢɱɢɧɟ ... ɲɚɝɨɜ ≤ ... f p x . no

0. ɇɟɭɤɚɡɚɧɧɵɟ ɩɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɪɚɡɦɟɪɨɜ: ɨɬɜɟɪɫɬɢɣ – ɇ4, ɜɚɥɨɜ – h4, ɨɫɬɚɥɶɧɵɯ ± (JT14/2)&. . Ɇɚɪɤɢɪɨɜɚɬɶ: ... (ɨɛɨɡɧɚɱɟɧɢɟ ɲɥɢɰɟɜɨɝɨ ɜɚɥɚ), ɤɥ...., ω t =.… Ɋ z = .… Ɋ6Ɇ5 (ɢɥɢ ɞɪɭɝɚɹ ɦɚɪɤɚ ɫɬɚɥɢ).

∗

HRC ɮɪɟɡ ɢɡ ɛɵɫɬɪɨɪɟɠɭɳɟɣ ɫɬɚɥɢ ɫ ɫɨɞɟɪɠɚɧɢɟɦ ɜɚɧɚɞɢɹ 3% ɢ ɛɨɥɟɟ, ɤɨɛɚɥɶɬɚ 5% ɢ ɛɨɥɟɟ ɧɚ 2-3 ɟɞɢɧɢɰɵ ɛɨɥɶɲɟ. ∗∗ Ɂɧɚɱɟɧɢɹ ɫɦ. ɜ ɬɚɛɥ. 5.2.

Ɍɚɛɥɢɰɚ 5.2. Ⱦɨɩɭɫɤɢ ɢ ɩɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɞɥɹ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɫ ɩɪɹɦɨɛɨɱɧɵɦ ɩɪɨɮɢɥɟɦ

ɉɪɨɜɟɪɹɦɵɣ ɩɚɪɚɦɟɬɪ Ⱦɢɚɦɟɬɪ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ Ɋɚɞɢɚɥɶɧɨɟ ɛɢɟɧɢɟ ɛɭɪɬɢɤɨɜ Ɍɨɪɰɨɜɨɟ ɛɢɟɧɢɟ ɛɭɪɬɢɤɨɜ Ɋɚɞɢɚɥɶɧɨɟ ɛɢɟɧɢɟ ɩɨ ɜɟɪɲɢɧɚɦ ɉɪɨɮɢɥɶ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ Ɋɚɡɧɨɫɬɶ ɫɨɫɟɞɧɢɯ ɨɤɪɭɠɧɵɯ ɲɚɝɨɜ ɇɚɤɨɩɥɟɧɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɨɤɪɭɠɧɨɝɨ ɲɚɝɚ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ ɇɚɩɪɚɜɥɟɧɢɟ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ ȼɢɧɬɨɜɚɹ ɥɢɧɢɹ ɮɪɟɡɵ ɧɚ ɨɞɧɨɦ ɨɛɨɪɨɬɟ Ɉɫɟɜɨɣ ɲɚɝ ɮɪɟɡɵ

Ɉɛɨɡɧɚɱɟɧɢɹ ɬɨɱɧɨɫɬɢ fd

fy

ft

f rd

a

fγ f no

Fp 0

fx

fh0

fpx

0


Ⱦɨɩɭɫɤɢ ɢ ɨɬɤɥɨɧɟɧɢɹ, ɦɤɦ, ɩɪɢ ɧɨɪɦɚɥɶɧɨɦ ɲɚɝɟ, ɦɦ ɫɜɵɲɟ ɫɜɵɲɟ ɫɜɵɲɟ ɫɜɵɲɟ ɞɨ 6,3 6,3 ɞɨ ɞɨ 9 ɞɨ 32 9 32

Ⱥ

ɇ5

ȼɢɋ Ⱥ ȼ ɋ Ⱥ ȼ ɋ Ⱥ ȼ ɋ Ⱥ ȼ ɋ Ⱥ ȼ ɋ Ⱥ

5 6 2 3 4 8 20 32 63 20 32 63 20 32 63 40

5 8 5 4 6 0 25 40 80 25 40 80 25 40 80 50

ɇ6 6 0 20 5 6 2 32 50 00 32 50 00 32 50 00 63

8 2 25 6 8 6 40 63 25 40 60 25 40 63 25 80

0 6 32 8 0 20 50 80 60 50 80 60 50 80 60 00

ȼ

63

80

00

25

60

ɋ

25

60

200

250

35

25 32

32 40

Ⱥ ȼ ɋ Ⱥ ȼ

0 6

2 20

± 80 ± 00 ± 25 6 25

ɋ

32

40

50

63

80

Ⱥ ȼ

±8 ± 2 ± 20

±9 ± 6 ± 25

± 0 ± 8 ± 28

± 0 ± 8 ± 32

± 2 ± 20 ± 40

2

ɩɪɨɞɨɥɠɟɧɢɟ ɬɚɛɥ 5.2. Ɉɬɤɥɨɧɟɧɢɟ ɨɫɟɜɨɝɨ ɲɚɝɚ ɦɟɠɞɭ «n» ɡɭɛɶɟɜ (ɲɚɝɨɜ): Pno 20 – n=2

fpx

Ⱥ

± 6

± 8

± 20

± 20

± 20

ȼ

± 25

± 32

± 36

± 36

± 40

ɋ

± 40

± 50

± 56

± 56

± 63

no

ɉɪɨɮɢɥɶ ɡɭɛɚ

ff0

Ɍɨɥɳɢɧɚ ɡɭɛɚ

TS 0

ɇɟ ɛɨɥɟɟ 2/3 ɜɟɥɢɱɢɧɵ ɩɨɥɹ ɞɨɩɭɫɤɚ ɧɚ ɬɨɥɳɢɧɭ ɡɭɛɚ ɜɚɥɚ ɧɚ ɜɵɫɨɬɟ 0,2 ɦɦ (ɨɬȺ ɤɥɨɧɟɧɢɹ ɬɨɥɶɤɨ ɜ ɩɥɸɫ) ɢ ɧɟ ɛɨɥɟɟ /3 ȼ ɜɟɥɢɱɢɧɵ ɩɨɥɹ ɞɨɩɭɫɤɚ ɧɚ ɬɨɥɳɢɧɭ ɡɭɛɚ ɋ ɜɚɥɚ ɧɚ ɜɵɫɨɬɟ 0,5 h 0 (ɨɬɤɥ. ɬɨɥɶɤɨ ɜ ɩɥɸɫ) ɇɟ ɛɨɥɟɟ /3 ɜɟɥɢɱɢɧɵ ɩɨɥɹ ɞɨɩɭɫɤɚ ɧɚ Ⱥ, ȼ, ɋ ɬɨɥɳɢɧɭ ɡɭɛɶɟɜ ɜɚɥɚ ɉɊɂɅɈɀȿɇɂə

ȼ ɩɪɢɥɨɠɟɧɢɹɯ ɞɚɧɵ ɩɪɢɦɟɪɵ ɪɚɫɱɟɬɚ ɧɟɤɨɬɨɪɵɯ ɡɭɛɨɪɟɡɧɵɯ ɢɧɫɬɪɭɦɟɧɬɨɜ ɢ ɪɚɛɨɱɢɯ ɱɟɪɬɟɠɟɣ ɷɬɢɯ ɢɧɫɬɪɭɦɟɧɬɨɜ. ɋ ɰɟɥɶɸ ɫɨɤɪɚɳɟɧɢɹ ɨɛɴɟɦɚ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ ɜ ɪɚɫɱɟɬɚɯ ɧɟ ɩɪɢɜɨɞɢɬɫɹ ɫɥɨɜɟɫɧɨɟ ɨɩɢɫɚɧɢɟ ɡɧɚɱɟɧɢɣ ɪɚɫɫɱɢɬɵɜɚɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɢ ɫɢɦɜɨɥɨɜ, ɜɯɨɞɹɳɢɯ ɜ ɮɨɪɦɭɥɵ. ɍɤɚɡɵɜɚɸɬɫɹ ɧɨɦɟɪɚ ɮɨɪɦɭɥ ɢ ɬɚɛɥɢɰ, ɩɨ ɤɨɬɨɪɵɦ ɩɪɨɢɡɜɨɞɢɬɫɹ ɪɚɫɱɟɬ. ɉɪɢ ɪɚɡɪɚɛɨɬɤɟ ɩɨɹɫɧɢɬɟɥɶɧɨɣ ɡɚɩɢɫɤɢ ɫɬɭɞɟɧɬ ɞɨɥɠɟɧ ɧɚɡɜɚɬɶ ɪɚɫɫɱɢɬɵɜɚɟɦɵɣ ɩɚɪɚɦɟɬɪ, ɩɪɢɜɟɫɬɢ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɚ, ɭɤɚɡɚɬɶ ɡɧɚɱɟɧɢɟ ɜɯɨɞɹɳɢɯ ɜ ɮɨɪɦɭɥɭ ɫɢɦɜɨɥɨɜ. Ɂɚɬɟɦ ɩɨɞɫɬɚɜɢɬɶ ɰɢɮɪɨɜɨɟ ɜɵɪɚɠɟɧɢɟ ɷɬɢɯ ɫɢɦɜɨɥɨɜ ɢ ɡɚɩɢɫɚɬɶ ɪɟɡɭɥɶɬɚɬ ɪɚɫɱɟɬɚ. ȿɫɥɢ ɬɪɟɛɭɟɬɫɹ ɨɤɪɭɝɥɟɧɢɟ, ɬɨ ɬɪɟɛɭɟɬɫɹ ɡɚɩɢɫɚɬɶ: ɉɪɢɧɢɦɚɸ (ɢɥɢ ɩɪɢɧɢɦɚɟɦ) ɢ ɭɤɚɡɚɬɶ ɰɢɮɪɨɜɨɟ ɡɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ ɩɪɨɟɤɬɢɪɭɟɦɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ. ȿɫɥɢ ɪɚɫɱɟɬ ɩɪɨɢɡɜɨɞɢɬɫɹ ɫ ɩɨɦɨɳɶɸ ɗȼɆ,

ɬɨ ɜ ɩɨɹɫɧɢɬɟɥɶɧɨɣ ɡɚɩɢɫɤɟ

ɞɨɥɠɧɵ ɛɵɬɶ ɩɪɢɜɟɞɟɧɵ ɧɚɩɟɱɚɬɚɧɧɵɟ ɧɚ ɩɪɢɧɬɟɪɟ ɜɟɥɢɱɢɧɵ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢ ɪɟɡɭɥɶɬɚɬɨɜ ɪɚɫɱɟɬɚ. ɇɟɨɛɯɨɞɢɦɨ ɩɪɢɜɟɫɬɢ ɪɚɫɲɢɮɪɨɜɤɭ ɫɢɦɜɨɥɨɜ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢ ɪɟɡɭɥɶɬɚɬɨɜ ɪɚɫɱɟɬɚ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɪɢɧɹɬɵɦ ɜ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɫɢɦɜɨɥɢɱɟɫɤɢɦ ɨɛɨɡɧɚɱɟɧɢɹɦ ɩɚɪɚɦɟɬɪɨɜ.

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ɉɪɢɥɨɠɟɧɢɟ . ɉɪɢɦɟɪ ɪɚɫɱɟɬɚ ɪɚɡɦɟɪɨɜ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɱɢɫɬɨɜɨɣ ɮɪɟɡɵ ɛɟɡ ɦɨɞɢɮɢɤɚɰɢɢ ɩɪɨɮɢɥɹ Ɋɚɫɫɱɢɬɚɬɶ ɢ ɫɩɪɨɟɤɬɢɪɨɜɚɬɶ ɱɟɪɜɹɱɧɭɸ ɮɪɟɡɭ ɞɥɹ ɧɚɪɟɡɚɧɢɹ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ m = 3 ɦɦ; α = 20 $ ; z = 30; h a = ; h *f = ,25; β = 0 $ ; ɯ = 0; ɫɬɟɩɟɧɢ ɬɨɱ*

ɧɨɫɬɢ 7 ɢ ɜɢɞɚ ɫɨɩɪɹɠɟɧɢɹ ȼ ɩɨ ȽɈɋɌɭ 643-8. Ɋɚɫɱɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ ɤɨɥɟɫɚ . (.) d =

mz 3 ⋅ 30 = = 90 ; cos β cos 0$

2. (.2) α t = α = 20$ ; 3. (.3) d b = d ⋅ cosα t = 90 ⋅ cos 20 $ = 84,572 ;

(

)

4. (.0) h a = h *a + x − Δy ⋅ m = ( + 0 − 0 ) ⋅ 3 = 3 ;

(

)

5. (.) d a = d + 2 h *a + x − ΔY ⋅ m = 90 + 2( + 0 − 0 ) ⋅ 3 = 96 ;

(

)

6. (.2) h = 2h *a + c − ΔY ⋅ m = (2 ⋅ + 0,25 − 0 ) ⋅ 3 = 6,75 ; 7. (.5) d f = d a − 2h = 96 − 2 ⋅ 6,75 = 62,5 ; 8. (ɬɚɛɥ..) E CS = 0,2; $ 9. (.6) Sn = 0,5π ⋅ m + 2x ⋅ m ⋅ tgα − ECS = 0,5 ⋅ π ⋅ 3 + 2 ⋅ 0 ⋅ tg20 − 0,2 = 4,592;

Ɋɚɫɱɟɬ ɪɚɡɦɟɪɨɜ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ . (Ɍɚɛɥ.2.) d ao = 2; d ɨɬɜ = 40; L = 2; 2. i = ; z 0 = 4; 3. γ = 0 $ ; α ɜ = 2 $ ; 4

4. (2.) K =

πd ao 3,4 ⋅ 2 tgα = ⋅ tg2 $ = 5,3 ; ɜ z0 4

ɉɪɢɧɢɦɚɟɦ K = 5;α ɜ = arctg

K ⋅ z0 5 ⋅4,0 = arctg = ,2552$ ; π ⋅ d ao π ⋅2

5. (2.2) K = 2K = 2 ⋅ 5 = 0 ; 6. (2.3) α wo = α = 20 $ ; 7. (2.4) h ao = h f = 3,75 ; * 8. (2.5) h f0 = ha + C ⋅ m = 3 + 0,25 ⋅ 3 = 3,75 ;

9. (2.6) h 0 = h ao + h f 0 = 3,75 + 3,75 = 7,5 ; 0. (2.7) r2 = 0,2 ⋅ m = 0,2 ⋅ 3 = 0,6 ; . (2.8) rɧ = 0,3 ⋅ m = 0,3 ⋅ 3 = 0,9 ; 2. (2.9) Pt 0 = π ⋅ m = π ⋅ 3 = 9,425 ; 3. (2.0) S t 0 = π ⋅ m − S n = π ⋅ 3 − 4,592 = 4,833 ; 4. (2.) H K = h 0 +

K + K 5 + 0 + 3 = 7,5 + + 3 = 8 ; Θ = 30 $ ; rɤ = 2 . 2 2

⎛ ⎞ $ ⎜ ⎟ ≥ 2 30'; arctg(tg,252° ⋅ sin 20°) ; 3,9 $ > 2,5 $ ; α α ⋅ arctg tg sin 5. (2.8) ⎜ ɜ w ⎟ 0⎠ ⎝

6. (2.9) D t = d ao − 2h ao − (0,4 ÷ 0,5)K = 2 − 2 ⋅ 3,75 − 0,4 ⋅ 5 = 02,5 ; 7. (2.20) ω t = arcsin

m ⋅ i 3 ⋅ = = ,677° = $ 40'38"; D t 02,5

8. ɇɚɩɪɚɜɥɟɧɢɟ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ – ɩɪɚɜɨɟ; ωɤ = ω t = $ 40'38"; ɧɚɩɪɚɜɥɟɧɢɟ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ - ɥɟɜɨɟ; 9. (2.2) Pz =

π ⋅ D t 3,4 ⋅ 2 = = 202; tgωɤ tg,677°

20. (2.22) Px 0 = Pto ⋅ i cos ωt = 9,425 ⋅ cos,677° = 9,429; 2. ψ = β + ω t = 0° + °40' = °40' ; 22. ɉɪɨɮɢɥɢɪɨɜɚɧɢɟ ɧɚ ɨɫɧɨɜɟ ɚɪɯɢɦɟɞɨɜɚ ɱɟɪɜɹɤɚ:

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(2.24) α oc = arctg

tgα wo tg 20° = arctg = 20,00776° ; cos ωt cos,677°

Pz − tgαoc 202− tg20,00776° = arctg = 20,04693° = 20°3' (2.25) αx R0 = arctg Pz − kz0tgαoc 202− 5⋅4⋅ tg20,00796° α x L 0 = arctg

Pz ⋅ tgα oc 202 ⋅ tg 20,00776° = = 9,96877° = 9°58' Pz + kz 0 tgα oc 202 + 5 ⋅ 4 ⋅ tg 20,00796°

23. (2.26) Poc.o = 24. (2.27) S oc.o =

Pt 0 cos ω t S to

cos ωt

=

=

9,425 = 9,429; cos,677°

4,833 = 4,835; cos,677°

25. (Ɍɚɛɥ.2.2) d = 70; l = 5; 26. (Ɍɚɛɥ.2.3) d = 60; l = 5; d b = arccos 84,572 = 28,2482° α = ; 27. (2.28) a arccos da 96 α

α tg 20° = 20° ; = arctg wo = arctg wto cos β cos 0°

l p = [(d a ⋅ sin α a − d ⋅ sin α ωto )⋅ cos α wto ⋅ cosψ ] cos β + 2 P oc .o = = [(96 ⋅ sin 28,2482 ° − 90 ⋅ sin 20° ) ⋅ cos 20°,677 ] cos 0° + 2 ⋅ 29,429 = 32,6 L ≥ (l p + 2l ) ; 32,6 + 2 5 = 42,6 ; (ɬɚɛɥ.2.) L = 2;2>42,6 ɉɪɢɧɢɦɚɟɦ L = 2. 28. (Ɍɚɛɥ.2.4) b n = 0C: C = 43,5H2; R = 0,9; ɞɨɩɭɫɤɚɟɦɨɟ ɫɦɟɳɟɧɢɟ ɩɚɡɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɨɬɜ. 0,09; 29. (2.30) l ɲ = 0,3 L = 0,3 ⋅ 2 = 34; 30. (2.3) d ɜ = d ɨɬɜ + 2 = 40 + 2 = 42. Ɋɚɛɨɱɢɣ ɱɟɪɬɟɠ ɮɪɟɡɵ ɩɪɢɜɟɞɟɧ ɧɚ ɪɢɫ. ɉ...

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7

ɉɪɢɥɨɠɟɧɢɟ 2. ɉɪɢɦɟɪ ɪɚɫɱɟɬɚ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ Ɋɚɫɫɱɢɬɚɬɶ ɢ ɫɩɪɨɟɤɬɢɪɨɜɚɬɶ ɱɟɪɜɹɱɧɭɸ ɮɪɟɡɭ ɞɥɹ ɧɚɪɟɡɚɧɢɹ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ m = 3 ɦɦ, α = 20° , z =20, h *a = , h *f = ,25, β = 0° , ɯ = 0, ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ 7 ɢ ɜɢɞɚ ɫɨɩɪɹɠɟɧɢɹ ȼ ɩɨ ȽɈɋɌ 643-8, ɧɚɯɨɞɹɳɟɝɨɫɹ ɜ ɡɚɰɟɩɥɟɧɢɢ ɫ ɤɨɥɟɫɨɦ z 2 = 40, ɯ 2 = 0. Ɋɚɫɱɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɫɨɩɪɹɠɟɧɧɵɯ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ . (.) d =

m ⋅ z 3 ⋅ 20 m ⋅ z 2 3 ⋅ 40 = = = 60; d 2 = = 20. cos β cos 0° cos β cos 0°

2. (.2) α t = arctg

m 2 tgα tg 20° = = 3. = arctg = 20° ; mt = cos β cos 0° cos β cos 0°

3. (.3) d b = d ⋅ cos α t = 60 ⋅ cos 20° = 56,38; d b 2 = d 2 ⋅ cos α t = 20 ⋅ cos 20° = 2,763. 4. (.4) α t w = α t = 20° ; ΔY = 0 . 5. (.5) invα t w = invα t + (.6) invα w = invα +

2( x + x 2 ) ⋅ tgα; α t w = α w ; z + z 2

2( x + x2 ) 2(0 + 0 ) ⋅ tgα = inv 20° + ⋅ tg 20° = inv 20° z + z 2 60

α w = 20° ; ΔY = 0 ;

(.8) a w = 0,5 m (z + z 2 ) = 0,5 ⋅ 3 (20+40) = 90. 6. (.0) h a = ( h *a + x - Δ y) ⋅ m = ( + 0 - 0) 3 = 3 ; h a 2 = 3. 7. (.) d a = d + 2m = 60 + 2 ⋅ 3 = 66; d a 2 = d 2 + 2m = 20 +2 ⋅ 3 = 26. * 8. (.2) h = (2 h *a + c - Δ y) m = (2 ⋅ + 0,25 - 0) ⋅ 3 = 6,75.

9. (.4) h f = h - h a = 6,75 - 3 = 3,75; h f 2 = 3,75. 0. (.5) d f = d - 2h = 66 - 2 6,75 = 52,5; 8

d f 2 = 26 - 2 ⋅ 6,75 = 2,5. . (.6) Sn = 0,5π ⋅ m − E CS = 0,5 ⋅ π ⋅ 3 − 0, = 4,62 ; Sn 2 = 0,5 ⋅ π ⋅ m − E CS = 0,5 ⋅ π ⋅ 3 − 0,2 = 4,592 . 2. (.7) ρ a = 0,5 d a2 − d 2b = 0,5 66 2 − 56,382 = 7,55 . 3. (.8) ρ p = a w ⋅ sin α t w − 0,5 d a2 2 − d 2b 2 = 90 ⋅ sin 20° − − 0,5 26 2 − 2,7632 = 2,673.

(

)

4. (.9) L = 0,5 d a2 − d 2b + d a2 2 − d 2b 2 − a w ⋅ sin α tw =

(

)

= 0,5 66 2 − 56,32 + 26 2 − 2,763 2 − 90 ⋅ sin 20° = 4,482 .

5. (.20) ΔL = 0,5 ⋅ m sin α tw = 0,5 ⋅ 3 sin 20° = ,36. 6. (.22) Ε = (L + 0,5L ) π ⋅ m ⋅ sin σ ⋅ cos α = = (4,482 + ,36 ) π ⋅ 3 ⋅ sin 20° = ,67, ɱɬɨ ɛɨɥɶɲɟ ,.

ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɡɭɛɨɲɟɜɢɧɝɨɜɚɧɢɟ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɜɨɡɦɨɠɧɨ ɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ ɞɨɩɭɫɬɢɦɨ. Ɋɚɫɱɟɬ ɪɚɡɦɟɪɨɜ ɩɪɨɮɢɥɹ ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ . d ao = 80; d ɨɬɜ = 32; L = 25; i = ; z 0 = 0; γ = 0° ; αɜ= 2; K=

πd ao 3,4 ⋅ 80 ⋅ tgα = ⋅ tg 9° = 3,98 , ɩɪɢɧɢɦɚɟɦ Ʉ = 4,0; ɬɨɝɞɚ ɜ z0 0

kz 4 ⋅ 0 α = arctg 0 = arctg = 9,04° ; K = ,5 ⋅ K = ,5 ⋅ 4 = 6. ɜ πd ao π ⋅ 80

ɉɪɢɧɢɦɚɟɦ Ʉ = 0; αɛɨɤ = arctg(tgαɜ ⋅ sinαwo ) = arctg(tg9,04° ⋅ sin20°) = 3,°; . 3,° > 2,5° .

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2. Ɍ.ɤ. d f < d b , ɬɨ (2.62) α wo min = arccos Ⱦɨɥɠɧɨ

ɛɵɬɶ α wo > α wo min (2.63).

df

= arccos

d b0

Ɋɚɡɧɢɰɚ

ɜ

52,5 = 2,38° . 56,38 ɭɝɥɚɯ

α wo

ɢ

α wo min ɧɟɡɧɚɱɢɬɟɥɶɧɚ, ɧɟɡɧɚɱɢɬɟɥɶɧɨɣ ɛɭɞɟɬ ɩɨɞɪɟɡɤɚ ɩɪɨɮɢɥɹ ɢ ɨɧɚ ɞɨɩɭɫɬɢɦɚ, ɬ.ɤ. ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹ ɞɚɥɶɧɟɣɲɚɹ ɨɛɪɚɛɨɬɤɚ ɲɟɜɢɧɝɨɜɚɧɢɟɦ. Ɉɤɨɧɱɚɬɟɥɶɧɨ α wo = 20° . 3. (2.65) Δ S = 0,07 ⋅ m + 0,08 = 0,007 ⋅ 3 + 0,08 = 0,3; ɩɪɢɧɢɦɚɟɦ Δ S = 0,4 ; (2.66) δ =

ΔS 0,4 = = 0,07. 2 2

4. (2.67) Pb = π ⋅ m ⋅ cos α = π ⋅ 3 ⋅ cos 20° = 8,856. 5. (2.68) Pwo =

Pb 8,856 = = 9,425. cos α wo cos 20°

6. (2.69) β wo = arcsin

sin 0° ⋅ cos 20° sin β ⋅ cos α = arcsin = 0° . cos 20° cos α wo

7. (2.70) α wt 0 = arctg

tgα wo tg 20° = arctg = 20° . cos β wo cos 0°

8. (2.7) d w =

d ⋅ cos α 60 ⋅ cos 20° = = 60 . cos α wto cos 20°

⎛ Sn + ΔS ⎞ + invα t − invα wto ⎟⎟ = 9. (2.72) S w = d w ⎜⎜ ⎝ d cos β ⎠ ⎛ 4,62 + 0,4 ⎞ = 60 ⋅ ⎜ + invα t − inv20° − inv20° ⎟ = 4,752 . ⎝ 60 ⋅ cos 0° ⎠ 0. (2.73) Sno = Pw 0 − S w = 9,425 − 4,752 = 4,673. . (2.74) h no =

d w − d f 2

=

60 − 52,5 = 3,75 . 2

2. (2.75) h 0 = h + 0,3m = 6,75 + 0,3 ⋅ 3 = 7,65 .

[(

)

]

3. (2.76) h y = h no − 0,5 ⋅ d w sin α wto − ρ p − δ ⋅ sin α wto = = 3,75 − [(0,5 ⋅ 60 ⋅ sin 20° − 2,673 − 0,007 ) ⋅ sin 20°] = ,7 ≈ ,8 ; 20

(2.77) c =

hy cos α wo

=

,8 = ,25; cos 20°

a = δ + 0,05 = 0,07 + 0,005 = 0,2; a

b=c–

r2 =

0,2 ⎞ = ,25 – tg(20° − 5° ) = 0,8; ⎛ − 5° ⎟ tg ⎜ α ⎟ ⎜ w o ⎠ ⎝

0, ⋅ m 0, ⋅ 3 = = 0,4. − sin α wo − sin 20°

Ɍ.ɤ. b > 0,5, ɬɨ ɩɪɢɧɢɦɚɸ ɮɨɪɦɭ ɭɫɢɤɚ ȼ. 4. ɉɪɨɜɟɪɤɚ ɜɟɥɢɱɢɧɵ ɭɬɨɥɳɟɧɢɹ ɭ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ ɧɚ ɜɨɡɦɨɠɧɨɫɬɶ ɱɪɟɡɦɟɪɧɨɝɨ ɩɨɞɪɟɡɚɧɢɹ ɧɨɠɟɤ ɡɭɛɚ ɤɨɥɟɫɚ. (2.78) h k = h no − [r2 ⋅ ( − sin α wo )] = 3,75 − [0,4( − sin 20° )] = 3,486 ; (2.79) rB =

(0,5d ) + (ρ 2

b

(2.80) α B = arccos

d b 2 ⋅ rB

+δ ) =

(0,5 ⋅ 56,38)2 + (2,673 + 0,07 )2

2

p

= arccos

= 28,323 ;

56,38 = 0,359328 ɪɚɞ 2 ⋅ 28,323

(2.8) ϕ = λ + invα wto − invα B = 0,359338 + inv20° − inv5,54438° = 0,3739398 (2.82) e t = [(0,5 d w – h k ) tg λ ] - (0,5 d w ⋅ϕ – h k ⋅ tg α wto ) = = [( 0,5 ⋅ 60 - 3,486) ⋅ tg 0,359338] - (0,5 ⋅ 60 ⋅ 0,3739398 – – 3,486 ⋅ tg 20° ) = 0.0 (2.83) e = e t ⋅ cos α wto ⋅ cos β w = 0,0 ⋅ cos 20° ⋅ cos 0° = 0,009 a > e - ɩɨɞɪɟɡɚɧɢɟ ɩɪɨɮɢɥɹ ɱɪɟɡɦɟɪɧɨɟ. ɉɨɷɬɨɦɭ ɩɪɢɧɢɦɚɸ ɚ = 0, ɬ.ɟ. ɢɫɤɥɸɱɚɸ ɭɬɨɥɳɟɧɢɟ ɩɪɢ ɜɟɪɲɢɧɟ ɡɭɛɚ ɮɪɟɡɵ. ȼ ɨɫɧɨɜɚɧɢɢ ɡɭɛɚ ɤɨɥɟɫɚ ɩɨɥɭɱɚɟɬɫɹ ɩɨɞɪɟɡ ɨɬ ɬɪɚɩɟɰɟɢɞɚɥɶɧɨɝɨ ɩɪɨɮɢɥɹ ɫ ɭɝɥɨɦ α wo = 20° . ɂ ɷɬɨɬ ɩɨɞɪɟɡ ɛɭɞɟɬ ɞɨɫɬɚɬɨɱɧɵɦ ɩɪɢ ɡɭɛɨɲɟɜɢɧɝɨɜɚɧɢɢ. 5. (2.84) h f = 0,075 ⋅ m + 0,35 = 0,075 ⋅ 3 + 0,35 = 0,57, ɩɪɢɧɢɦɚɸ h f = 0,6; f = 0,05 ⋅ m = 0,05 ⋅ 3 = 0,5 (2.85) α ɮɨ = α wo + 0° = 20° + 0° = 30° ;

2

(2.86) d A = d a − 2h f = 66 − 2 ⋅ 0,6 = 64,8 ; (2.87) α A = arccos

d w ⋅ cos α wo dA

(2.88) α ɮ A = arccos (2.89) h ɮo = =

= arccos

d w ⋅ cos d ɮɨ dA

60 ⋅ cos 20° = 29,5335°; 64,8

= arccos

60 ⋅ cos 30° = 36,69038°; 64,8

d (invα wo − invα A − invα ɮɨ + invα ɮȺ ) 2(tgα ɮɨ − tgα wo )

+ h no =

60(inv20° − inv29,5335° − inv30° + inv36,69038) + 3,75 = 5,834 2(tg30° − tg 20°) (2.90) α a ɨɫɧ = arccos

d w ⋅ cos α wo d a

= arccos

⎛ Sw (2.9) Sa ɨɫɧ = d a ⎜ + invα wo − invα a ɨɫɧ ⎜ dw ⎝

60 ⋅ cos 20° = 3,3223° 66 ⎞ ⎟= ⎟ ⎠

⎛ 4,752 ⎞ = 66⎜ + inv20° − inv3,3223° ⎟ = 2,28 ⎝ 60 ⎠ (2.92) ⎞ ⎛ Sw ⎛ 4,752 ⎞ + inv20° − inv29,5335° ⎟ = SA = d A ⎜ + invα w 0 − invα A ⎟ = 64,8⎜ ⎜ dw ⎟ ⎝ 60 ⎠ ⎝ ⎠ =2,788; (2.93) α ɚɮ = arccos

d w ⋅ cos α ɮɨ d a

= arccos

60 ⋅ cos 30° = 38,06644° ; 66

⎛S ⎞ (2.94) Sɚɮ = d a ⎜⎜ A + invα ɮɚ − invα ɚɮ ⎟⎟ = ⎝ dA ⎠ ⎛ 2,788 ⎞ = 66⎜ + inv36,903° − inv38,06644° ⎟ = ,94; ⎝ 64,8 ⎠ (2.95) q =

Sa ɨɫɧ − Sɚɮ 2

=

2,28 − ,94 = 0,06; 2

q - f = 0,06 - 0,5 = - 0,04.

22

(2.8) r ɧ = 0,3 ⋅ m = 0,3 ⋅ 3 = 0,9. Ⱦɨɩɨɥɧɢɬɟɥɶɧɵɣ ɪɚɫɱɟɬ ɩɨɤɚɡɚɥ, ɱɬɨ ɮɥɚɧɤ ɫ ɪɚɡɦɟɪɚɦɢ α ɮɨ = 35° ɢ h ɮɨ = 5,9 ɨɛɟɫɩɟɱɢɬ ɫɪɟɡ ɭ ɝɨɥɨɜɤɢ ɡɭɛɚ ɤɨɥɟɫɚ h f = 0,6 ɢ f = 0,5. 6. (2.3) h ao = h f = 3,75. 7. (2.4) D t = d ao − 2h ao − 0,4K = 80 − 2 ⋅ 3,75 − 0,4 ⋅ 5,5 = 70,3 8. (2.5) ω t = arcsin

m ⋅i 3 ⋅ = arcsin = 2,44579° = 2° 26'45". Dt 70,3

ɇɚɩɪɚɜɥɟɧɢɟ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ - ɩɪɚɜɨɟ. 9. (2.6) H ɤ = h 0 +

K + K 4+6 + 2 = 7,65 + + 2 = 3,65. 2 2

ɉɪɢɧɢɦɚɸ ɇ ɤ = 4. 20. Θ = 30° 2. (2.7) r = π ⋅ (d ao − 2H ɤ ) 0z = 3,4 ⋅ (80 − 2 ⋅ 8 ) 0 ⋅ 0 = ,38. ɉɪɢɧɢɦɚɸ r = ,5. 22. ɇɚɩɪɚɜɥɟɧɢɟ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ ɧɨɪɦɚɥɶɧɨɟ ɤ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɟ, ɬ.ɟ. ɥɟɜɨɟ ɢ (2.8) ωɤ = ω t = 2° 26'. (2.9) Pz =

π ⋅ D t 3,4 ⋅ 70,3 = = 568. tgωɤ tg 2°26'

23. (2.20) D w o = d ao − 2h no − 0,4 ⋅ K = 80 − 3,75 − 0,4 ⋅ 5,5 = 70,3. ⎛ D ⎞ ⎛ 70,3 ⎞ ⋅ tg 2,44579° ⎟ = 2° 26'45". 24. (2.2) ω = arctg⎜⎜ t ⋅ tgω t ⎟⎟ = arctg⎜ ⎝ 70,3 ⎠ ⎝ D wo ⎠ 25. (2.22) Pxo =

Pwo ⋅ i 9,425 ⋅ = = 9,433. cos ω cos 2,44579°

26. (2.23) ψ = β + ω t = 0 + 2°26' = 2° 26'. 27. ɉɪɨɮɢɥɢɪɨɜɚɧɢɟ ɧɚ ɨɫɧɨɜɟ ɤɨɧɜɨɥɸɬɧɨɝɨ ɱɟɪɜɹɤɚ. ɉɪɨɮɢɥɶ ɡɚɞɚɟɬɫɹ ɜ ɧɨɪɦɚɥɶɧɨɦ ɤ ɜɢɬɤɚɦ ɮɪɟɡɵ ɫɟɱɟɧɢɢ. 28. (2.24) Pto = π ⋅ m = π ⋅ 3 = 9,425.

23

29. (2.25) S to = Sno + 2 ⋅ tgα wo (h ao − h no ) = 4,673 + 2 tg 20° ⋅ (3,75 − 3,75)= 4,673. 30. (2.26) Poc.o =

Pwo 9,425 = = 9,433. cos ω cos 2,244579°

3. (Ɍɚɛɥ.2.3) d = 50, l = 5; (Ɍɚɛɥ.2.4) b n = 8C, C = 34,8H2, R = 0,9 +0,3 ; L = 25; (2.30) l ɲ = 0,3 L = 0,3 ⋅ 25 = 40; d ɜ = d ɨɬɜ + 2 = 32 + 2 = 34.

Ɋɚɛɨɱɢɣ ɱɟɪɬɟɠ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ ɩɪɢɜɟɞɟɧ ɧɚ ɪɢɫ.ɉ 2.. Ɍɟɯɧɢɱɟɫɤɢɟ ɬɪɟɛɨɜɚɧɢɹ ɤ ɮɪɟɡɟ ɫɥɟɞɭɸɳɢɟ: . ɇRC ɗ 64...65. 2. ɇɚ ɜɫɟɯ ɩɨɜɟɪɯɧɨɫɬɹɯ ɮɪɟɡ ɧɟ ɞɨɥɠɧɨ ɛɵɬɶ ɬɪɟɳɢɧ, ɡɚɭɫɟɧɰɟɜ ɢ ɫɥɟɞɨɜ ɤɨɪɪɨɡɢɢ. 3. ɇɟɩɨɥɧɵɟ ɜɢɬɤɢ ɩɪɢɬɭɩɢɬɶ ɞɨ ɬɨɥɳɢɧɵ ɜɟɪɯɧɟɣ ɱɚɫɬɢ ɡɭɛɚ ɧɟ ɦɟɧɟɟ 0,5 ɦɨɞɭɥɹ. 4. ɉɪɹɦɨɥɢɧɟɣɧɨɫɬɶ ɢ ɧɚɤɥɨɧ ɥɢɧɢɢ ɩɟɪɟɫɟɱɟɧɢɹ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɩɥɨɫɤɨɫɬɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɨɫɢ ɮɪɟɡɵ, ɧɚ ɪɚɛɨɱɟɣ ɜɵɫɨɬɟ ɡɭɛɚ ≤ 0,04. 5. ɇɚɤɨɩɥɟɧɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɨɤɪɭɠɧɨɝɨ ɲɚɝɚ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ ≤ 0,08. 6. Ɉɬɤɥɨɧɟɧɢɟ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬ ɧɨɦɢɧɚɥɶɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ, ɨɬɧɟɫɟɧɧɨɟ ɤ 00 ɦɦ ɞɥɢɧɵ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɮɪɟɡɵ, ≤ ± 0,. 7. ɉɨɝɪɟɲɧɨɫɬɶ ɡɚɰɟɩɥɟɧɢɹ ɨɬ ɡɭɛɚ ɤ ɡɭɛɭ ≤ 0,02. 8. ɉɨɝɪɟɲɧɨɫɬɶ ɡɚɰɟɩɥɟɧɢɹ ≤ 0,022. 9. ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ∅ 32ɇ6 ɞɨɥɠɧɨ ɛɵɬɶ ɜɵɞɟɪɠɚɧɨ ɧɚ ɞɥɢɧɟ 24 ɦɦ ɤɚɠɞɨɝɨ ɩɨɫɚɞɨɱɧɨɝɨ ɩɨɹɫɤɚ. 0. Ⱦɨɩɭɫɬɢɦɨɟ ɫɦɟɳɟɧɢɟ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ∅ 32ɇ6 ≤ 0,09.

24

. ɇɟɭɤɚɡɚɧɧɵɟ ɩɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɪɚɡɦɟɪɨɜ: ɨɬɜɟɪɫɬɢɣ - ɇ4, ɜɚɥɨɜ- h4, ɨɫɬɚɥɶɧɵɯ + (IT4)/2. 2. Ɇɚɪɤɢɪɨɜɚɬɶ: m = 3, α = 20° , ɤɥ.ȼ, ω t = 2° 26', P z = 568, Ɋ6Ɇ5Ʉ5.

25

ɉɪɢɥɨɠɟɧɢɟ 3. ɉɪɢɦɟɪ ɪɚɫɱɟɬɚ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ Ɋɚɫɫɱɢɬɚɬɶ ɢ ɫɩɪɨɟɤɬɢɪɨɜɚɬɶ ɱɟɪɜɹɱɧɭɸ ɮɪɟɡɭ ɞɥɹ ɧɚɪɟɡɚɧɢɹ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ m = 3 ɦɦ, α = 20° , z = 40, h *a = , h *f = ,25; β = 0° , x = 0, ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ 7 ɢ ɜɢɞɚ ɫɨɩɪɹɠɟɧɢɹ ȼ ɩɨ ȽɈɋɌ 643-8, ɧɚɯɨɞɹɳɟɝɨɫɹ ɜ ɡɚɰɟɩɥɟɧɢɢ ɫ ɤɨɥɟɫɨɦ z 2 = 20, ɯ 2 = 0 Ɋɚɫɱɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɫɨɩɪɹɠɟɧɧɵɯ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ . (.) d =

mz 2 3 ⋅ 20 m ⋅ z 3 ⋅ 40 = = = 20 ; d 2 = = 60. cos β cos 0° cos β cos 0°

2. (.2) α t = arctg

tgα m 3 tg 20° = = arctg = 20° ; m t = =3 cos β cos β cos 0° cos 0°

3. (.3) d b = d ⋅ cos α t = 20 ⋅ cos 20° = 2,763; d b 2 = d ⋅ cos α t = 60 ⋅ cos 20° = 56,38. 4. (.4) α tw = α t = 20° ; Δ Y = 0. 5. (.5) invα tw = invα t +

2(x + x 2 ) tgα ; α tw = α t = 20° . z + z 2

6. (.6) α w = α = 20° . 7. (.8) a w = [0,5 ⋅ m(z + z 2 ) ⋅ cos α t ] (cos α tw ⋅ cos β ) = = [0,5 ⋅ 3 ⋅ (40 + 20 )cos 20°] cos 20° ⋅ cos 0° = 90. * 8. (.0) ha = (ha + x − Δy) ⋅ 3 = ( + 0 − 0)⋅ 3 = 3;

ha2 = (ha* + x2 − Δy ) ⋅ 3 = ( + 0 − 0) ⋅ 3 = 3. 9. (.) d a = d + 2m = 20 + 2 ⋅ 3 = 26; d a 2 = d 2 + 2m = 60 + 2 ⋅ 3 = 66.

(

)

* 0. (.2) h = 2ha + c − Δy ⋅ 3 = (2 ⋅ + 0,25 − 0 )⋅ 3 = 6,75.

. (.4) = h f = h − h a = 6,75 − 3 = 3,75; h f 2 = 3,75. 26

2. (.5) d f = d a − 2h = 26 − 2 ⋅ 6,75 = 2,5; d f 2 = d a 2 − 2h = 66 − 2 ⋅ 6,75 = 52,5. 3. (.6) Sn = 0,5 ⋅ π ⋅ m − E CS = 0,5 ⋅ π ⋅ 3 − 0,2 = 4,592 ; Sn 2 = 4,62. 4. (.7) ρ a = 0,5 d a2 − d 2b = 0,5 26 2 − 2,7632 = 28,09. 5. (.8) ρ p = aw ⋅ sin α tw − 0,5 d a2 − d b2 = 90 ⋅ sin 20° − 0,5 66 2 − 56,382 = 2

=3,627.

2

(

)

6. (.9) L = 0,5 d a2 − d 2b + d a2 2 − d 2b 2 − a w ⋅ sin α tw =

(

)

= 0,5 26 2 − 2,7632 + 66 2 − 56,382 − 90 ⋅ sin 20° = 4,482.

7. (.20) ΔL = 0,5 ⋅ m sin α tw = 0,5 ⋅ 3 sin 20° = ,36. 8. (.22) ε = L + 0,5L π ⋅ m ⋅ sin σ ⋅ cosα = = (4,482 + ,36 ) π ⋅ 3 ⋅ sin 90° ⋅ cos 20° = ,67.

ɒɟɜɢɧɝɨɜɚɧɢɟ ɜɨɡɦɨɠɧɨ. Ɋɚɫɱɟɬ ɪɚɡɦɟɪɨɜ ɩɪɨɮɢɥɹ ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ . d ao = 80; d ɨɬɜ = 32; L = 25; i = 1; z 0 = 0; γ = 0° ; α ɜ = 9° ; K=

π ⋅ d ao 3,4 ⋅ 80 ⋅ tgα ɜ = ⋅ tg9° = 3,98 . ɉɪɢɧɢɦɚɸ Ʉ = 4° ; Ʉ = 6. z0 0

α ɛɨɤ = arctg(tgα ɜ ⋅ sin α wo ) = arctg(tg9,04° ⋅ sin 20° ) = 3,° .

ȼɟɥɢɱɢɧɚ ɡɚɞɧɟɝɨ ɭɝɥɚ ɧɚ ɛɨɤɨɜɨɣ ɪɟɠɭɳɟɣ ɤɪɨɦɤɟ ɞɨɫɬɚɬɨɱɧɚɹ. df 2,5 = 3,9° ; 2. Ɍ.ɤ. d f < d b , ɬɨ (2.62) α wo min = arccos = arccos d b 2,763 3,9° < 20° . ɋɥɟɞɨɜɚɬɟɥɶɧɨ, α wo = 20° . 3. (2.65) ΔS = 0,07 ⋅ m + 0,08 = 0,07 ⋅ 3 + 0,08; ɩɪɢɧɢɦɚɟɦ S = 0,4; (2.66) δ =

ΔS 0,4 = = 0,07. 2 2

4. (2.67) Pb = π ⋅ m ⋅ cos α = π ⋅ 3 ⋅ cos 20° = 8,856. 5. (2.68) Pwo =

Pb 8,856 = = 9,425. cos α wo cos 20° 27

6. (2.69) β wo = arcsin

sin β ⋅ cos α sin 0° ⋅ cos 20° = arcsin = 0° . cos α wo cos 20°

7. (2.70) α wto = arctg

tgα wo tg 20° = arctg = 20° . cos 0° cos β w

8. (2.7) d w =

d ⋅ cos α 20 ⋅ cos 20° = = 20 . cos α wto cos 20°

⎛ Sn + ΔS ⎞ + invα t − invα wto ⎟⎟ = 9. (2.72) S w = d w ⎜⎜ ⎝ d ⋅ cos β ⎠ ⎛ 4,592 + 0,4 ⎞ = 20 ⋅ ⎜ + inv20° − inv20° ⎟ = 4,732. ⎝ 20 ⋅ cos 0° ⎠ 0. (2.73) Sno = Pwo − S w = 9,425 – 4,732 = 4,693. . (2.74) h no =

d w − d f 2

=

20 − 2,5 = 3,75. 2

2. (2.75) h 0 = h + 0,3 ⋅ m = 6,75 + 0,3 ⋅ 3 = 7,65/

[(

)

]

3. (2.76) h y = hno − 0,5d w ⋅ sin α wto − ρ p − δ ⋅ sin α wto = = 3,75 − [(0,5 ⋅ 20 ⋅ sin 20° − 3,627 − 0,07 ) ⋅ sin 20°] = = ,674 ≈ ,67. (2.77) C =

hy coaα wo

=

,67 = ,78; cos 20°

a = δ + 0,05 = 0,07 + 0,05 = 0,2; b=c– r2 =

a

tg(α wo − 5° )

= ,78 –

0,2 = ,33; tg(20° − 5° )

0, ⋅ m 0, ⋅ 3 = = 0,43 ; − sin α wo − sin 20°

ɉɪɢɧɢɦɚɟɦ rɝ= 0,5; ɬ.ɤ. b > 0,5, ɬɨ ɩɪɢɧɢɦɚɟɦ ɮɨɪɦɭ ɭɫɢɤɚ ȼ. 4. ɉɪɨɜɟɪɤɚ ɜɟɥɢɱɢɧɵ ɭɬɨɥɳɟɧɢɹ ɭ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ ɧɚ ɜɨɡɦɨɠɧɨɫɬɶ ɱɪɟɡɦɟɪɧɨɝɨ ɩɨɞɪɟɡɚɧɢɹ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ

[ (

)]

(2.78) hɤ = hno − rɝ ⋅ − sin α wo = 3,75 − [0,5( − sin 20°)] = 3,4

28

(0,5d ) + (ρ

(2.79) rB =

2

b

+δ ) = 2

p

(0,5 ⋅ 2,763)2 + (3,627 + 0,07 )2 =

=58,02; (2.80) α B = arccos

λ = arccos

d b 2⋅ r ɜ

0,5d w − h ɤ rB

= arccos

= arccos

2,763 2,763 = arccos = 3,65305° ; 58,02⋅ 2 6,042

0,5 ⋅ 20 − 3,4 = 2,7067° = 0,22773 ɪɚɞ; 58,02

(2.8) ϕ = λ + invα wto − invα B = 0,227737 + inv20° − inv3,65305° = = 0,2320635; ⎡⎛ ⎤ ⎛ ⎞ ⎞= ⎜ ⎟ = − ⋅ λ ⋅ ϕ − h ⋅ tgα e 0 , 5 d h tg ⎢ ⎥ − ⎜ 0,5 ⋅ d ⎟ (2.82) t ⎜ ⎟ w ɤ w ɤ wto ⎠ ⎠ ⎣⎢⎝ ⎦⎥ ⎝ = [(0,5 ⋅20 − 3,4)tg 0,227737 ]− (0,5 ⋅20 ⋅ 0,2320635 − 3,4 ⋅ tg 20°) = 0,075;

(2.83) e = e t ⋅ cos α wto ⋅ cos β w = 0,075 ⋅ cos 20° ⋅ cos 0° = 0,07. Ⱦɨɥɠɧɨ ɛɵɬɶ a < e; a = 0,2, e = 0,07. ɉɪɢɧɢɦɚɟɦ a = e = 0,07. Ɍɨɝɞɚ b = ,78 –

0,07 = ,5. Ⱦɥɹ ɭɦɟɧɶɲɟɧɢɹ ɬɪɭɞɧɨɫɬɟɣ ɢɡɝɨɬɨɜɥɟɧɢɹ tg5°

ɢɧɫɬɪɭɦɟɧɬɚ ɥɭɱɲɟ ɩɪɢɧɹɬɶ ɜɚɪɢɚɧɬ ɨɮɨɪɦɥɟɧɢɹ ɭɫɢɤɚ – δ ɩɨ ɪɢɫ. 2.5. Ɂɞɟɫɶ c = ,78, h y = ,67, a = 0,07, rɝ= 0,05. 5. (2.84) h f = 0,075 ⋅ m + 0,35 = 0,075 ⋅ 3 + 0,35 = 0,57; ɩɪɢɧɢɦɚɸ h f = 0,6; f = 0,05 ⋅ m = 0,05 ⋅ 3 = 0,5. (2.85) α ɮɨ = α wo + 0° = 20° + 0° = 30° ; (2.86) d A = d a − 2h f = 26 − 2 ⋅ 0,6 =24,8; (2.87) α A = arccos

d w ⋅ cos α wo

(2.88) α ɮA = arccos (2.89) h ɮɨ = =

dA d w ⋅ cos α ɮɨ dA

=

20 ⋅ cos 20° = 25,378° ; 24,8

= arccos

20 ⋅ cos 30° = 33,62° 24,8

d (invα wo − invα A − invα ɮɨ + invα ɮȺ ) 2(tg30° − tg 20°)

+ h no =

20(inv20° − inv25,378° − inv30° + inv33,62° ) + 3,75 = 5,964; 2(tg30° − tg 20°) 29

(2.90) α ɚɨɫɧ

d w ⋅ cosα w0 20 ⋅ cos 20$ = arccos = arccos = 26,49854$ d a 26

S = d ( w + invα − invα )= Wo ɚɨɫɧ a d ɚ w ɨɫɧ (2.9) 4,732 = 26( + inv20° − inv26,49854°) = 2,303 20 S

⎛ S w

⎞ ⎛ 4,732 ⎞ + invα w0 − invα A ⎟ = 24,8⎜ + inv 20° − inv 25,378° ⎟ = ⎟ ⎝ 20 ⎠ ⎠

(2.92) S A = d A ⎜⎜

⎝ d w

2,862; (2.93) α a ɮ = arccos

d w ⋅ cos α ɮɨ d a

= arccos

20 ⋅ cos 30° = 94,4334° ; 26

⎛S ⎞ (2.94) Sɚɮ = d a ⎜⎜ A + invα ɮɚ − invα ɚɮ ⎟⎟ = ⎝ dA ⎠ ⎞ ⎛ 2,862 = 26⎜ + inv33,62° − inv34,4334° ⎟ = 2,075: ⎠ ⎝ 27,8

(2.95) q =

Sa ɨɫɧ − Sɚɮ 2

=

2,303 − 2,075 = 0,4; 2

q < f ɧɚ 0,036 ɦɦ. ɉɨɷɬɨɦɭ ɩɪɢɧɢɦɚɟɦ α ɮɨ = 35° , h ɮɨ = 6 ɦɦ. (2.8) rH = 0,3 ⋅ m = 0,3 ⋅ 3 = 0,9. 6. (2.3) h ao = h f = 3,75. 7. (2.4) D t = d ao - 2 h ao - 0,4 ⋅ k = 80 - 2 ⋅ 3,75 - 0,4 ⋅ 5,5 = 70,3. 8. (2.5) ω t = arcsin

3 ⋅ m ⋅i = arcsin = 2,44579° = 2° 26'45". 70,3 Dt

ɇɚɩɪɚɜɥɟɧɢɟ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ – ɩɪɚɜɨɟ. 9. (2.6) H ɤ = h 0 +

K + K 4+6 + 2 = 7,65 + + = 3,05. 2 2

ɉɪɢɧɢɦɚɟɦ ɇ ɤ = 4. 20. Θ = 30° . 30

2. (2.7) r = π ⋅ (d ao − 2 H ɤ ) / 0 z 0 = 3,4(80 - 2 ⋅ 8 ) / 0 ⋅ 0 = ,38, ɩɪɢɧɢɦɚɸ r = ,5 22. ɇɚɩɪɚɜɥɟɧɢɟ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ ɧɨɪɦɚɥɶɧɨɟ ɤ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɟ, ɬ.ɟ. ɥɟɜɨɟ ɢ (2.8) ω ɤ = ω t = 2° 26'. (2.9) Pz =

π ⋅ D ɤ 3,4 ⋅ 70,3 = = 568. tgωɤ tg 2°26'

23. (2.20) Dwo = d ao − 2hno − 0,4 ⋅ k = 80 − 2 ⋅ 3,75 − 0,4 ⋅ 5,5 = 70,3 ⎛ D ⎞ ⎛ 70,3 ⎞ ⋅ tg 2,44579° ⎟ = 2° 26'45" 24. (2.2) ω = arctg⎜⎜ t ⋅ tgω t ⎟⎟ = arctg⎜ ⎝ 70,3 ⎠ ⎝ D wo ⎠ 25. (2.22) Pxo =

Pwo ⋅ i 9,725 ⋅ = = 9,433. cos ω cos 2,44579°

26. (2.23) ψ = β + ω t = 0° + 2°26' = 2° 26' 27. ɉɪɨɮɢɥɢɪɨɜɚɧɢɟ ɧɚ ɨɫɧɨɜɟ ɤɨɧɜɨɥɸɬɧɨɝɨ ɱɟɪɜɹɤɚ ɢ ɩɨɷɬɨɦɭ ɧɚ ɪɚɛɨɱɟɦ ɱɟɪɬɟɠɟ ɩɪɨɮɢɥɶ ɡɭɛɶɟɜ ɩɨɤɚɡɵɜɚɟɬɫɹ ɬɨɥɶɤɨ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɤ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ. 28. (2.24) Pto = π ⋅ m = π ⋅ 3 = 9,425. 29.

(2.25)

S to = S no + 2 ⋅ tgα wo (h ao − h no ) = 4,693 + 2 ⋅ tg 20° ⋅ (3,75 − 3,75 )=

=4,693 30. (2.26) Poc.o =

Pwo 9,425 = = 9,433. cos ω cos 2,44579°

3. (Ɍɚɛɥ.2.3) d = 50; l = 5; (Ɍɚɛɥ.2.4) b n = 8C; C = 34,8 H2; R = 0,9 +0,3 ; L = 25; (2.30) l ɲ = 0,3 L = 0,3 25 = 40 d ɜ = d ɨɬɜ + 2 = 32 + 2 = 34 Ɋɚɛɨɱɢɣ ɱɟɪɬɟɠ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ ɩɨɤɚɡɚɧ ɧɚ ɪɢɫ.ɉ 3..

3

32

Ʉ ɮɪɟɡɚɦ ɩɪɟɞɴɹɜɥɹɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɬɟɯɧɢɱɟɫɤɢɟ ɬɪɟɛɨɜɚɧɢɹ. . HRC ɷ 64...66. 2. ɇɚ ɜɫɟɯ ɩɨɜɟɪɯɧɨɫɬɹɯ ɮɪɟɡ ɧɟ ɞɨɥɠɧɨ ɛɵɬɶ ɬɪɟɳɢɧ, ɡɚɭɫɟɧɰɟɜ ɢ ɫɥɟɞɨɜ ɤɨɪɪɨɡɢɢ. 3. ɇɟɩɨɥɧɵɟ ɜɢɬɤɢ ɩɪɢɬɭɩɢɬɶ ɞɨ ɬɨɥɳɢɧɵ ɜɟɪɯɧɟɣ ɱɚɫɬɢ ɡɭɛɚ ɧɟ ɦɟɧɟɟ 0,5 ɦɨɞɭɥɹ. 4. ɉɪɹɦɨɥɢɧɟɣɧɨɫɬɶ ɢ ɧɚɤɥɨɧ ɥɢɧɢɢ ɩɟɪɟɫɟɱɟɧɢɹ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɩɥɨɫɤɨɫɬɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɨɫɢ ɮɪɟɡɵ, ɧɚ ɪɚɛɨɱɟɣ ɜɵɫɨɬɟ ɡɭɛɚ ≤ 0,04. 5. ɇɚɤɨɩɥɟɧɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɨɤɪɭɠɧɨɝɨ ɲɚɝɚ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ ≤ 0,08. 6. Ɉɬɤɥɨɧɟɧɢɟ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬ ɧɨɦɢɧɚɥɶɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ, ɨɬɧɟɫɟɧɧɨɟ ɤ 00 ɦɦ ɞɥɢɧɵ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɮɪɟɡɵ ≤ ± 0,. 7. ɉɨɝɪɟɲɧɨɫɬɶ ɡɚɰɟɩɥɟɧɢɹ ɨɬ ɡɭɛɚ ɤ ɡɭɛɭ ≤ 0,02. 8. ɉɨɝɪɟɲɧɨɫɬɶ ɡɚɰɟɩɥɟɧɢɹ ≤ 0,022. 9. ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ∅ 32ɇ6 ɞɨɥɠɧɨ ɛɵɬɶ ɜɵɞɟɪɠɚɧɨ ɧɚ 24 ɦɦ ɞɥɢɧɵ ɤɚɠɞɨɝɨ ɩɨɫɚɞɨɱɧɨɝɨ ɩɨɹɫɤɚ. 0. Ⱦɨɩɭɫɤɚɟɦɨɟ ɫɦɟɳɟɧɢɟ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜ. ∅ 32ɇ6 ≤ 0,09. . ɇɟɭɤɚɡɚɧɧɵɟ ɩɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɪɚɡɦɟɪɨɜ: ɨɬɜɟɪɫɬɢɣ - ɩɨ ɇ4, ɜɚɥɨɜ - h4, ɨɫɬɚɥɶɧɵɯ + (IT4)/2. 2. Ɇɚɪɤɢɪɨɜɚɬɶ: m =3, α = 20° , ɤɥ.ȼ, ω t = 2° 26' P z = 568, P6M5K5.

33

ɉɪɢɥɨɠɟɧɢɟ 4. ɉɪɢɦɟɪ ɪɚɫɱɟɬɚ ɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɞɨɥɛɹɤɚ ɞɥɹ ɧɚɪɟɡɚɧɢɹ ɡɭɛɶɟɜ ɤɨɥɟɫ Ɋɚɫɫɱɢɬɚɬɶ ɢ ɫɩɪɨɟɤɬɢɪɨɜɚɬɶ ɞɨɥɛɹɤ ɞɥɹ ɧɚɪɟɡɚɧɢɹ ɡɭɛɶɟɜ ɤɨɥɟɫɚ ɫ ɩɚɪɚɦɟɬɪɚɦɢ: α = 20° , m= 3 ɦɦ, z = 25, h *a = , h *l = 2, h *f = ,25; β = 22° , x =0; 7 ɫɬ. ɬɨɱɧɨɫɬɢ ɫ ɫɨɩɪɹɠɟɧɢɟɦ «ɋ» ɩɨ ȽɈɋɌ 6-443-8, ɧɚɯɨɞɹɳɟɝɨɫɹ ɜ ɡɚɰɟɩɥɟɧɢɢ ɫ ɡɭɛɱɚɬɵɦ ɤɨɥɟɫɨɦ m = 3 ɦɦ, z 2 = 75, ɯ 2 = 0 ɬɨɣ ɠɟ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ. Ɉɩɪɟɞɟɥɟɧɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ . (.) d =

mz 2 mz 3 ⋅ 75 3 ⋅ 25 = = = 80,89 ; d 2 = = 242,67. cos β cos 22° cos β cos 22°

2. (.2) α t = arctg

tgα tg 20° = arctg = 2,4327° ; cos β cos 22°

m t = m cos β = 3 cos 22° = 3,2356.

3. (.3) d b = d ⋅ cos α t = 80,890 ⋅ cos 2,4327° = 75,296; d b 2 = d 2 ⋅ cos α t = 242,67 ⋅ cos 2,4327° = 225,889. 4. (.4) x = x 2 = 0 : α tw = α t = 2,4327° . 5. (.8) a w = [0,5 ⋅ m ⋅ (z + z 2 ) ⋅ cos α t ] (cos α tw ⋅ cos β ) = = [0,5 ⋅ 3 ⋅ (25 + 75 ) ⋅ cos 2,4327°] (cos 2,4327° ⋅ cos 22° ) = 6,78.

6. (.9) Δ ɭ = 0.

(

)

7. (.) d a = d + 2 h *a + x − Δy ⋅ m = 80,89 + 2( + 0 − 0 ) ⋅ 3 = 86,89;

(

)

d a 2 = d 2 + 2 h *a + x 2 − Δy ⋅ m = 242,67 + 2( + 0 − 0 ) ⋅ 3 = 248,67.

(

)

8. (.2) h = 2h *a + c* − Δy ⋅ m = (2 ⋅ + 0,25 − 0 ) ⋅ 3 = 6,75. 9. (.5) d f = d a − 2h = 86,89 − 2 ⋅ 6,75 = 73,39; d f 2 = d a 2 − 2h = 248,67 − 2 ⋅ 67 = 235,7. 0. (.6) Sn = 0,5 ⋅ π ⋅ m + 2 ⋅ x ⋅ m ⋅ tgα − E cs = 0,5 ⋅ π ⋅ 3 + 2 ⋅ 0 ⋅ tg 20° − 0,07 = = 4,642; 34

Sn 2 = 0,5 ⋅ π ⋅ m + 2 ⋅ x 2 ⋅ m ⋅ tgα − E cs 2 = 0,5 ⋅ π ⋅ 3 + 2 ⋅ 0 ⋅ tg 20° − 0,08 = 4,632. . (.7) ρ a = 0,5 d a2 − d 2b = 0,5 86,89 2 − 75,296 2 = 2,68. 2. (.8) ρ p = a w ⋅ sin α wt − 0,5 ⋅ d a2 2 − d 2b 2 = 6,78 ⋅ sin 2,4327° − − 0,5 ⋅ 248,67 2 − 225,889 2 = 7,28.

Ɋɚɫɱɟɬ ɞɨɥɛɹɤɚ -5. Ɉɩɪɟɞɟɥɟɧɢɟ z 0 , d 0 , d b 0 ,β , α t, α ɭɫɬ ɞɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɫɥɭɱɚɹ ɩɪɨɢɡɜɟɞɟɧɨ ɜ ɩɪɢɦɟɪɟ ɜ ɩɨɞɪɚɡɞɟɥɟ 3. «Ɉɩɪɟɞɟɥɟɧɢɟ ɱɢɫɥɚ ɡɭɛɶɟɜ ɢ ɢɫɯɨɞɧɨɝɨ ɪɚɫɫɬɨɹɧɢɹ ɡɭɛɨɪɟɡɧɨɝɨ ɞɨɥɛɹɤɚ». ɉɪɢɦɟɦ z 0 = 3. Ɍɨɝɞɚ d 0 = 00,92996; d b 0 = 93,87927; D ɤ = 00; α ɭɫɬ = 20,6; β = 22,8638° = 22° 5'50" = 0,3990487 ɪɚɞ; α t = 2,55428° = 0,37693 ɪɚɞ. ɇɨɜɵɟ ɡɧɚɱɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɛɭɞɭɬ d =

mz mz 2 3 ⋅ 25 3 ⋅ 75 = = 8,395 ; d 2 = = = 244,85 ; cos β cos 22,8638° cos β cos 22,8638°

α t = arctg

tgα tg 20° = arctg = 2,55427° = 0,376929 ɪɚɞ; cos β cos 22,8638°

m t = m / cosβ = 3 / cos 22,8638° = 3,2558; d b = d ⋅ cos α t = 8,395 ⋅ cos 2,55427° = 75,703; d b 2 = d 2 ⋅ cos α t = 244,85 ⋅ cos 2,55427° = 227,09; α tw = α t = 2,55427° ; a w = [0,5 ⋅ m ⋅ (z + z 2 ) ⋅ cos α t ] (cos α tw ⋅ cos β ) = = [0,5 ⋅ 3 ⋅ (25 + 75 ) ⋅ cos 2,554727°] (cos 2,554727 ⋅ cos 22,8638° )= 62,790;

(

)

Δ ɭ = 0; d a = d + 2 h *a + x − Δy ⋅ m = 8,395 + 2( + 0 − 0 ) ⋅ 3 = 87,395;

(

)

d a 2 = d 2 + 2 h *a + x 2 − Δy ⋅ m = 244,85 + 2( + 0 − 0 ) ⋅ 3 = = 250,85; 35

(

)

h = 2h *a + c* − Δy ⋅ m = (2 ⋅ + 0,25 − 0 ) ⋅ 3 = 6,75; d f = d a − 2h = 87,395 − 2 ⋅ 6,75 = 73,895; d f 2 = d a 2 − 2h = 250,85 − 2 ⋅ 6,75 = = 236,685; Sn = 0,5 ⋅ π ⋅ m + 2 ⋅ x ⋅ m ⋅ tgα − E cs = 0,5 ⋅ π ⋅ 3 + 2 ⋅ 0,3 ⋅ tg 20° − 0,07 = 4,642; Sn 2 = 0,5 ⋅ π ⋅ m + 2 ⋅ x 2 ⋅ m ⋅ tgα − E cs 2 = 0,5 ⋅ π ⋅ 3 + 2 ⋅ 0,3 ⋅ tg 20° − 0,08 = 4,632; ρ = 0,5 d 2 − d 2 = 0,5 87,395 2 − 75,703 2 = 2,834 a a b

ρ p = a w ⋅ sin α tw − 0,5 d a2 2 − d 2b 2 = 62,790 ⋅ sin 2,55427° − − 0,5 ⋅ 250,85 2 − 227,09 2 = 7,332.

Ɋɚɫɱɟɬ ɩɚɪɚɦɟɬɪɨɜ ɞɨɥɛɹɤɚ ɜ ɢɫɯɨɞɧɨɦ ɫɟɱɟɧɢɢ 6. (3.0) d 'ao = d + d 0 − d f = 8,395 + 00,930 - 73,895 = 08,430. 7. (3.) S'no = π ⋅ m − Sn = π ⋅ 3 − 4,642 = 4,78277 = 4,783. 8.

(3.2)

(

)

α 'ato = arccos d bo d 'ao = arccos(93,87927 08,430 = 30,03298° ) =

= 0,524743 ɪɚɞ.

(

) (

)

' = d ' ⎡⎛ S ' d ⋅ cos β ⎞⎟ + tgα − α − ⎛⎜ tgα ' − α ' ⎞⎟⎤ = 9. (3.3) S ato a0 ⎢⎣⎜⎝ no 0 t t ⎝ ato ato ⎠⎥⎦ ⎠

= 08,43[(4,783 (00,92996 ⋅ cos 0,3990487° )) + (tg 0,37693° − 0,37693) − − (tg 0,524743° − 0,524743 )]= ,767.

Ɉɩɪɟɞɟɥɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɤɨɪɪɟɤɰɢɢ ɢ ɢɫɯɨɞɧɵɯ ɪɚɫɫɬɨɹɧɢɣ 0. (3.4) Sato min = =

(

(

)

0,2594 ⋅ m − 0,0375 cos β =

)

0,2594 ⋅ 3 − 0,0375 cos 0,3990487° = 0,934.

. (3.5) γ = 5° ; α ɜ = 6° ;

(

)

(3.6) α n = arctg tgα ɜ ⋅ sin α = arctg (tg 6° ⋅ sin 20°) = 2,058° ; 2,058° < 2°30 . ɉɪɢɧɢɦɚɟɦ α n = 2,5° . Ɍɨɝɞɚ α ɜ = arctg(tgα n sin α ) = arctg (tg 6° / sin 20°) = 7° 6'= 7, 275° 36

' = d 'ao + 2 ⋅ x '0 ⋅ m = 08,43 + 2 ⋅ x '0 ⋅ 3 . 2. (3.8) d 'ao

(

)

(

)

'' '' '' 3. (3.9) α ato = arccos d bo d ao = arccos 93,87927 d ao .

(

)(

)

= d ' ' ⋅ ⎡⎢⎛⎜ S ' + 2 x ' ⋅ m ⋅ tgα ⎞⎟ d ⋅ cos β + tgα − d − 4,5. S ato ao ⎣⎝ no t t 0 ⎠ 0 min − ⎛⎜ tgα ' ' − α ' ' ⎞⎟⎤ . ato ato ⎠⎥⎦ ⎝

'' 0 , 934= d ao

[(4,783+ 2⋅x0 ⋅3⋅tg 0,349058) ( 00,92996⋅cos 0,9243) +

(

'' −α '' +( tg 0 , 37693− 0 , 37693 ) − tgα ato ato

)].

Ɋɟɲɟɧɢɟ ɬɪɚɧɫɰɟɧɞɟɧɬɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɧɚ ɗȼɆ ɫ ɬɨɱɧɨɫɬɶɸ 0,0 ɞɚɟɬ ɪɟɡɭɥɶɬɚɬ ɏ '0 = 0,7656. 6.

(3.23)

(

)

a 'H = x '0 ⋅ m tgα b cos β = (0,7656 ⋅ 3 tg 7,275 ° ) ⋅ cos 22,8638 =

=6,578.

a' = 7. (3.24) H

=

S ⎞ ⎛ ato ⎜ ' min ⎟ ⋅ d ' − S ⎟ ⎜ ato cos β ⎟ ao ⎜ ⎠ ⎝ 2⎛⎜ d ' ⋅ tgα' − S' ⎞⎟tgα − ato ato ⎠ ɜ ⎝ ao

( , 767 −0 , 934

(dao′ )

=

2

d

⋅C

0

cos 22 ,8638° ) ⋅08, 43

2( 08 , 43⋅tg 30 , 03298° −, 767 ) tg 7 , 275° −

08, 432 ⋅0 ,073 = 30,7 00 , 93

ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɚɫɱɟɬɚ ɡɧɚɱɟɧɢɟ ɚ 'H ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɨɫɯɨɞɢɬ ɡɧɚɱɟɧɢɟ, ɩɨɥɭɱɟɧɧɨɟ ɧɚ ɗȼɆ ɩɪɢ ɬɨɱɧɨɦ ɪɚɫɱɟɬɟ. ɇɨ, ɤɚɤ ɛɭɞɟɬ ɜɢɞɧɨ ɞɚɥɟɟ, ɢɫɯɨɞɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɥɢɦɢɬɢɪɭɟɬ ɧɟ ɜɟɥɢɱɢɧɚ ɚ 'H , ɚ ɜɟɥɢɱɢɧɚ ɚ 'H' . 8. (3.25) C = tg {β + arctg[(tg α ɜ ⋅ tgα )/( - tg γ ⋅ tgα ɜ )]} – – tg {β – arctg [(tg α ɜ ⋅ tgα ) /( – tg γ ⋅ tgα ɜ )]} = 37

= tg { 22,8638° + arctg [(tg 7,275° ⋅ tg 20° )/( – tg)]} – – tg { 22,8638° – arctg [(tg 7,275° ⋅ tg 20° )/( – tg 5° ⋅ tg 7,275° )]} = = 0,073. 9. (3.26)

(

)(

⎡2 d + d b b 0 d f − 2ρ p ⋅ sin α t = arccos⎢ ⎢ d b + d 2 + d f2 − d 2b − 4ρ 2p b0 0 ⎣

(

' α 'tw

)

)⎤⎥ ⎥ ⎦

=

⎡ 2(75,703 + 93,872)(73,895 − 2 ⋅ 7,332 ⋅ sin 2,55427° )⎤ = = arccos⎢ 2 2 2 2 ⎥ ( ) + + − − ⋅ 75 , 03 93 , 72 73 , 895 93 , 872 4 7 , 332 ⎦ ⎣ = 22,7563° = 0,3964625 ɪɚɞ. 20. (3.27) a 'H' =

(tgα =

'' tw

)

' − α 'tw − tgα t + α t (d + d 0 ) − 2 ⋅ x ⋅ tgα t ⋅ m = c

(tg0,3964625 − 0,3964625 − tg0,376929 + 0,376929) = 5,523. 0,073

2. Ɍɚɤ ɤɚɤ a 'H − a 'H' > 0, ɬɨ a H = a 'H' = 5,52. '' = arctg[2( ρ a + ρ0 )/(d b + d b 0 )]; ρ10 = 5 ; 22. (3.28) α 'tw

= arctg [2(2,834 + 5)/(75,703 + 93,872)] = 7,568° = 0,30654 ɪɚɞ. 23. Ɍɚɤ ɤɚɤ d f < d b , ɬɨ (3.29) α IV tw

(

)

⎡ 2d f d b + d b 0 = ars cos ⎢ ⎢⎣ d b + d b 0 2 + d f2 − d 2b 0

(

)

⎤ ⎥= ⎥⎦

⎤ ⎡ 2 ⋅ 73,895(75,703 + 93,872) = 9,42866° = 0,64443 ɪɚɞ. = arccos⎢ 2 2 2⎥ ( ) + + − 75 , 703 93 , 872 73 , 892 93 , 872 ⎦ ⎣ III IV 24. Ɍɚɤ ɤɚɤ α tw − α tw > 0, ɬɨ α twc = α tw = 0,30654 ɪɚɞ. III

25. (3.30) ac = =

(tgαtwc − α twc − tgαt + α t )(d + d 0 )− 2 xtgα ɜ ⋅ m C

=

(tg0,30654 − 0,30654 − tg0,37693 + 0,37693)(8,395 + 00,93) = – 4,55. 0,073

26. (3.3) H = a H − a C = 5,52 + 4,55 = 20,07. 38

27. (Ɍɚɛɥ.3.) B p = 2. Ɍɚɤ ɤɚɤ H > B p ɢ a H < 0,5 ⋅ B p , ɬɨ Ⱥ = ɚ H = 5,52, ɩɪɢɧɢɦɚɟɦ Ⱥ = 5,5 ɦɦ. Ɉɩɪɟɞɟɥɟɧɢɟ ɱɟɪɬɟɠɧɵɯ ɪɚɡɦɟɪɨɜ ɞɨɥɛɹɤɚ 28. (3.32) invα twɧ = invα t + x 0 = A ⋅ tgα

ɜ

(

)

2tgα x + x 2 ; z +z 2

(m ⋅ cos β ) = 5,5 ⋅ tg 7,275° (3 ⋅ cos 22,8638°)= 0,254;

inv α twH = tg0,376929 – 0,376929 + 2 ⋅ tg 0,3490658(0 + 0,254)/(25 + 3) = = 0,02238; α twH = 0,3966. 29. Ɍɚɤ ɤɚɤ H > B p , ɬɨ B= ȼ′Ɋ = 2. (3.33) x oc = (A – B p/ ) tgα B / (m ⋅ cos β )= = (5,5 − 2 ) ⋅ tg 7,275° / (3 ⋅ cos 22,8638° )= – 0,3. invα twc ɮɚɤɬ = invα t + 2 ⋅ tgα ⋅ (x + x oc ) (z + z 2 ) = tg 0,376929 − 0,376929 + + 2 ⋅ tg 0,3490658° (0 − 0,3) (25 + 3) = 0,04925;

α twc ɮɚɤɬ = 0,349925 ɪɚɞ = 20,00338 9° . 30. Ɍɚɤ ɤɚɤ ɇ > B p , ɬɨ ȼ = ȼ p/ + ȼ ɢɡɧ = 2 + 8 = 20. / + A ⋅ c ⋅ cos β = 4,783 + 5,5 ⋅ 0,073 ⋅ cos 22,8638° = 5,344. 3. (3.35) S no = S no

+d b b 0 − d = 75,703 + 93,872 − 73,895 = 09,96. 32. (3.36) d ao = f cos 0 , 3966 cos α twɧ d

⎛ d ⋅ cos α t 33.(3.37) α ato = arccos⎜⎜ 0 d ao ⎝

⎞ 00,93 ⋅ cos 2,55428° ⎟⎟ = arccos = 0,54706 ɪɚɞ. 09 , 96 ⎠

⎛ Sno ⎞ ⎛ d ⋅ tgβ ⎞ ⎛ 5,344 ⎟⎟ = ⎜ + + invα t − invα ato ⎟⎟ ⋅ cos⎜⎜ arctg ao Sano = d ao ⎜⎜ ⋅ ° ⋅ β d cos d 00 , 93 cos 22 , 8638 ⎝ ⎝ 0 ⎠ ⎝ ⎠ 0 + tg 0,3766929 − 0,376929 − tg 0,54706 − 0,54706 ) ⋅ 09,96 ⋅ tg 0,3990487 ⎞ ⎛ ⋅ cos⎜ arctg ⎟ = ,4439 ≈ ,44 ɦɦ. 00,93 ⎝ ⎠ 39

34. (3.38) h ao =

d ao − d 0 09,96 − 00,93 = = 4,50 ɦɦ. 2 ⋅ cos γ 2 ⋅ cos 5°

35. (3.39) h 0 = h + 0,3 m = 6,75 + 0,3 3 = 7,65. 36. (3.40) α ɛɨɤ

tgα ⋅ tgα ɜ = arctg − tgγ ⋅ tgα

= arctg ɜ

tg 7,275° ⋅ tg 20° = 2,69° = 2° 4'. − tg 5° ⋅ tg 7,275°

(tgα + tgγ ⋅ tgα ɛɨɤ )cos α ɛɨɤ = cos(β − α ɛɨɤ ) ( ° + ° ⋅ °) ⋅ ° = ° = ° 0'23". = arctg ( ° + °) ( α + γ ⋅ α ) α = (3.43) α =

(β − α ) ( ° + ° ⋅ °)⋅ ° = ° = ° 23'26". = arctg = ° − °) ( 37. (3.42) α min = arctg

38. (3.45) =

(

⋅ α = ⋅ ° = 93,977.

)

39. (3.47) α = α β = ( ° °) = ° = = ° 53'.

∗− ηα∗− ξ0)⋅ χοσβ⎤ ⎡ ( 4 η λ 40. (3.48) δ Λ 0 = αρχτγ⎢⎣τγατ− ζ0⋅ σιν2ατ ⎥⎦ = =

= arctg 5' = 0,2592482 .

=

(3.49)

= = 2,448.

= 4. (3.50) + 0,259482)

= (tg 0,25948 2'. 40

– 0,259482 +

42. (3.5)

9'.

43. (3.52) A = A / cos

= 5,5 / cos 22,8638

= 5,968.

44. (3.54) = 2,75829

45';

(3.55) = 2,66576

40'.

! "#$ d 0,7 d

= 44,45; b = 0; D = 70; b = ; B = 20; D =

% &&' ( ) = 75.

* ! ( ( + , + #

4

42

43

+! * - $

, m = 3, z = 25, h = ; h = ,25, h = 2,

, x = 0,7

! ./0 12/ ,3 "45, 6( 7 z2= 75, x= 0 , h = , h = ,25, h = 2.

. (.)

; % 8"39 " #

2. (.2) 3. (.3)

= 74,425; = 223,277.

4. (.4) x = x = 0;

= 0,3695352.

5. (.7)

=

=

=59,626.

6. (.9) x = x = 0:

y = 0.

7. (.0)

= 3; = 3.

8. (.3) h =

= 6,75.

9. (.)

= 85,83; = 245,44.

0. (.5)

= 72,33;

44

= 23,94. . (.4)

= 6,75 – 3 = 3,75; = 6,75 – 3 = 3,75.

2. (.6)

= = 4,67.

3. (.8) = 6,693. 4. (.9)

=

= = 4,666. 5. (.20)

= ,246.

6. (.2)

= ,243595

= ,897.

7. (.22) ,59& : ,, / -( ! .

.

# ; ( ,? @

-

-

.

(

" 8? !

+

' &

&

= 45,765.

( > ,?

= 20,460.

48

# + > #?$

;

80,79 + 202,592 – 20,460 – 72,33 = – 0,002; – 0,002 < 0,6. D- d 85 ( d = 7,53.

80,79 + 202,592 – 20,460 – 7,53 = 0,8; 0,8 > 0,6. = 4,346.

26.

= 7,53;

27. (

(

(

= 7,53 – 4,346 = 3,84. =

28.

!

" !!

; ;

=

=

=

= ,56.

( 85 ( ,3 >85 #? % ,3 = , 3 % 88 H 8,' - 29.

'

= 44,94. ;

= 5,008.

;

; = = ,79. + ( - l ( : l = 0,7 % = ,79 –

= % 8# : 8,

50

C - 6$ d = 80,056 + 202,37 – 209,75 – 0,6 = 72,023; % "59 h "59 = "& % 8, 6 = 3,99;

= 7,75.

? - 30. (4.44)

= 200,67;

(4.45)

;

(4.46)

;

(4.47)

;

(4.48)

(4.49)

;

= 79,325;

(4.50)

=

=

= 47,594;

(4.5)

=

= 4,442. (4.52)

= 206,847. 5

(4.53)

= 79,325 + 200,67 – 206,847 – 72,023= ,25;

,,# : 83 / ! - - (4.54)

= 4,442 –

=

24,953. = 95,975.

(4.55) C!

' ,9 9& : ,9 /

! - 2 6 - 3. (4.58) (4.59)

; = 5,027;

(4.60)

=

= 95,4 (

) = 6,88;

(4.6)

= 2,344;

(4.62) d = T G " % #" G " % " I = 5,5; = 90,922 ,

(4.63) ) % ,98

= 4,84294° = 4°50'.

(4.64) 37. b = 20.

52

"5 J , , >- ( 7 -( ? "$ K % ,8' l = = 8&' ,# D b2 % L G , % # 39. (4.65)

= 5,007.

40. (4.66)

= 4,022.

* ! ( ( - + , + #

53

55

+! 3

! * -7( M $ I45N"3O5N 8P,,N&Q5 # ? L = 8C; C = 34,8H2; R = 0,9 + 0,3; 6 ≤ 0,09. 29. (5.62)

= 79,6.

30. (5.63)

37';

3. (5.64)

37'; (5.65)

.

= 3950. = 5,0.

32. (5.66) 33.

= 7,796 – 2[9,2 (0,394376 – 0,89769) – – (9,

in 0,394376 – 3,62) cos 0,344376] = 6,877.

* ! -7 +6..

$ , STU 3"3 # ! 6 7 " 6 6 - 7 2 -( !

0,.

(- !( -(

0,2.

3 2 ! H G 8,# & 2

+ 0,005.

5 2 60

0,05.

9 2 ( -( " -(

0,056.

,8 $ , 4 Y,

JT4/2.

,, A$ I45 N "3O5 N 8P,, N Jf5 / > -? 37', P = 3950, P6M5.

6

62

+! &

" * -7( $ )45 N 3# N &#Q& N ,#Y5 >)45 N 3# N &#

x 2

? A

8R " 8 d = 57,8 + ! . (.32)

= 70,97.

2. (.34) d = d = 57,8. 3. (.35) b = b

+ 0,25 T = 2 – 0,027 + 0,2

4. (5.)

027 = ,98. = 70,208;

r = 35,04. = 0,7475

5. (5.2) 6. (5.3) a =

7. (5.4)

= 5,99.

= 6,204.

8. (5.7)

=

=

= 0,5407

9. (5.9)

% 8,&, & 63

0. (5.2)

= 70,208 – 6,204 = 64,004; = 59,04; % 8,55#53 '

(5.3)

% 8#8 "#5 ' % 8 3,,9# '

(5.4)

% 838""" ' (5.5)

= = 35,04(0,4692 – 0,7475) – (35,04 in 0,4692 – – 5,99 cos 0,4692 = ,545 = = 35,04(0,60333 – 0,7475) – (35,04 in 0,60333 – – 5,99)cos 0,60333 = 3,69

(5.6)

0,4692 – – 5,99 in 0,4692 = 4,286; 0,60333 –

– 5,99 in 0,60333 = 7,902; (5.7)

= 22,43; (5.8)

= – 5,387;

64

(5.9)

= 23,068.

,, 2 (- ( ! (5.20) A =

= 0,4270605;

= – 0,6732

= 0,5707594

(5.2)

=

= 35,04 0,5707594 – 0,7475) – (35,04 in 0,5707594 – – 5,99 cos 0,5707594 = 3,097 = = 35,04 0,283366 – 0,7475) – (35,04 in 0,283366 – – 5,99)cos 0,283366 = 0,2556 0,5707594 – – 5,99 in 0,5707594 = 7,0098 20,283366 – – 5,99 in 0,283366 = ,069 (5.22)

= =

= – 0,02.

C-

> 0,08.

( ( !

65

2. (5.24)

= 67,06; = 70,208 – 6,208 = 64,004; = 0,79485; = 0,88286 = 0,346807; = 0,4692;

= = 35,04 0,346807 – 0,7475) – (35,04 in 0,346807 – – 5,99 cos 0,346807 = 6,548545 – 5,5878906 = 0,5669639; = = 35,04 0,4692 – 0,7475) – (35,04 in 0,4692 – – 5,99 cos 0,4692 = 0,70225 – 8,62535 = ,544874 0,346807 – – 5,99 in 0,346807 = 4,055494 – 2,035965 = 2,095264;

– 5,99 in 0,4692 = 6,952968 – 2,6656459 = 4,2863222; 6,79878;

= – 3,6046083; = 7,0402 A=

= 0,335364;

66

0,063229;

= 0,4376; = 0,256967;

– 0,7475) – (35,04 in 0,4376 – 5,99) os 0,4376 = ,0669593;

– 0,7475) – (35,04 in 0,256967 – 5,99)

os 0,256967 = 0,657593; 0,4376 –

– 5,99 in 0,4376 = 3,2662; 0,25448 – – 5,99 in 0,25448 = 0,7450629; = =

= – 0,009 = – 7,04 = 0,02; = 0,02; 2/3 T = 0,08 88#, = 88,5 % 888# (- -

(5.25)

= 59,0408; = 0,204328 ; = 0,60333 ;

(5.26)

67

(5.27)

=

= 35,04 (0,60333 – 0,7475) – (35,04 in 0,60333 – 5,99 cos 0,60333 = = 3,695; 0,60333 – 5,99 in 0,60333 = 7,902345; % ,8" ," ' % 8 &9 , ' (5.29)

=

= 37,46658 + ,544874 = 34,78588 4,2863222)= – 2,99888 A =

= 0,6630473;

0,4224364

= 0,53965

– 0,7475) – (35,04 in 0,53965 – 5,99)

os 0,53965 = 2,470975

0,53965 – 5,99 in 0,53965 = = 5,9920246 = =

– 37,46658 = 0,05;

88, H 88,5 ( R . 68

3. (5.3) os 0,5407 = 0,345786; (5.32) d

= 30,696;

= 6,392; d = 62; d

< d,

4. (5.35)

= 27,57; = 5,532.

5. ( ,? d = 40; d = 60; d

= 40; d = 42; f = ,5; f = 2; l

(5.36) z = 4 6. (5.37)

; % 8,393,3 '

(5.38)

% 885 9" ' = = (5.42) h = C 7. (5.43)

= 0,25; = 0,8. ; (5.44) K =

V % 3 ' 8. (5.45)

tg

= 6,67;

= 2. = 6,204 + 0,25 + 0,8 = 7,254.

,9 > 3? V ! $ Y % ,

69

= 3,5

(5.49)

= = 0,55; (5.49) r = 2 = 7,254 + = 8,254

20. (5.5) h = 2. (5.55)

;

.

D - ( +=

22. (5.57)

8,5;

W = 9;

; r = 2. = 0,4.

23. (5.59) C = 24. (5.60) L =

= + 23,5 = 02

= X % , 8 25. (5.6) l = 0,25 L = 0,2

40 = 35

#3 > # ? L = 0C; C = 43,5H2; R = 0,9 + 0,3' 6

= 24,342

27. (5.62) (5.63)

3'; ;

28. (5.66)

0,09.

3'; (5.65)

= 552. = 27,640.

70

29. = 0,338.

–

* ! -7 +&, 6$ , STU 3"3 # ! 6 7 " 6 6 - 7 2 -( !

0,04.

(- !( -( 3 2 ! & 2

0,08.

0,08.

+ 0,009.

5 2 9 2 ( -( # -(

0,025.

0,02.

,8 $ 4 , 4 Y, 4 ± (IT4)/2. ,, A$ )45 N 3# N &#Q& N ,#Y5 ' M *3A

7

3', P = 552,

/+@/2V Z@ [*M D*\ 72

, / ( U ] + @M ^( #4 A$ A- ,953 5 2. _ U -( 74 * ($ / ] @M ^ A$ A- ,9& ,38 " 12/ ,3 "45, + 7 C A$ 1 ///* ,998 35 4. / /F< #354&3 / -7 U ( "8 @ A$ @4 ,9&3 9 12/ ,,"9458 / -7 * 4 A$ @4 ,958 9 3 2 11 M ` / A$ A- ,95" ##" & ;M @7 A$

Расчёт И Проектирование Зуборезных Инструментов

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