Кафедра ДМ 09 04 2013 / Киреев - Расчёт И Проектирование Зуборезных Инструментов
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Киреев
ȼȼȿȾȿɇɂȿ
Ʉ ɱɢɫɥɭ ɧɚɢɛɨɥɟɟ ɫɥɨɠɧɵɯ ɢ ɞɨɪɨɝɢɯ ɦɟɬɚɥɥɨɪɟɠɭɳɢɯ ɢɧɫɬɪɭɦɟɧɬɨɜ ɨɬɧɨ-
ɫɹɬɫɹ ɡɭɛɨɪɟɡɧɵɟ ɢɧɫɬɪɭɦɟɧɬɵ. ȼ ɩɨɫɨɛɢɢ ɩɪɢɜɟɞɟɧɵ ɦɟɬɨɞɵ ɪɚɫɱɟɬɚ ɢ ɩɪɨɟɤɬɢ-
ɪɨɜɚɧɢɹ 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, ɧɚ-
ɩɪɢɦɟɪ, 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 ɪɚɫ-
ɱɟɬɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɜɨɡɦɨɠɧɨɫɬɶɸ ɩɪɢɦɟɧɟɧɢɹ ɫɬɚɧɞɚɪɬɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ ɞɥɹ ɨɛɪɚ-
ɛɨɬɤɢ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɢ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ.
Ɉɩɬɢɦɚɥɶɧɨɣ ɤɨɧɫɬɪɭɤɰɢɟɣ ɡɭɛɨɪɟɡɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ ɹɜɥɹɟɬɫɹ ɬɚɤɚɹ ɤɨɧɫɬ-
ɪɭɤɰɢɹ, 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 ɡɭɛɨɪɟɡ-
ɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ ɬɚɤɠɟ ɪɚɫɫɦɨɬɪɟɧ ɜ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ. Ɋɟɲɟɧɢɟ ɜɨɩɪɨɫɚ ɨɩɬɢɦɢ-
ɡɚɰɢɢ ɤɨɧɫɬɪɭɤɰɢɢ, ɤɚɤ ɩɪɚɜɢɥɨ, ɭɫɩɟɲɧɨ ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɨ ɩɪɢ ɩɪɨɟɤɬɢɪɨ-
ɜɚɧɢɢ 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 ɦɨɧɨ-
ɥɢɬɧɨɝɨ ɡɭɛɨɪɟɡɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ.
5
. ɂɋɏɈȾɇɕȿ ȾȺɇɇɕȿ, ɋɉɊȺȼɈɑɇȺə ɂɇɎɈɊɆȺɐɂə ȾɅə ɉɊɈȿɄɌɂɊɈȼȺɇɂə ɁɍȻɈɊȿɁɇɕɏ ɂɇɋɌɊɍɆȿɇɌɈȼ ɂ ɊȺɋɑȿɌ ȾɈɉɈɅɇɂɌȿɅɖɇɕɏ ɌȿɏɇɈɅɈȽɂɑȿɋɄɂɏ ɉȺɊȺɆȿɌɊɈȼ ɁɍȻɑȺɌɕɏ ɄɈɅȿɋ ɂ ɒɅɂɐȿȼɕɏ ȼȺɅɈȼ
ȼ ɡɚɞɚɧɢɢ ɧɚ ɤɭɪɫɨɜɨɟ ɢɥɢ ɞɢɩɥɨɦɧɨɟ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɜ ɤɚɱɟɫɬɜɟ ɢɫ-
ɯɨɞɧɵɯ ɞɚɧɧɵɯ ɩɪɢɜɨɞɹɬɫɹ ɩɚɪɚɦɟɬɪɵ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ ɢ ɫɨɩɪɹɠɟɧɧɨɝɨ ɤɨ-
ɥɟɫ ɡɭɛɱɚɬɨɣ ɩɚɪɵ: ɱɢɫɥɨ ɡɭɛɶɟɜ ɨɛɪɚɛɚɬɵɜɚɟɦɨɝɨ z1 ɢ ɫɨɩɪɹɠɟɧɧɨɝɨ z2 ɤɨ-
ɥɟɫ; ɦɨɞɭɥɶ m; ɭɝɨɥ ɩɪɨɮɢɥɹ ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɞɢɚɦɟɬɪɟ α; ɤɨɷɮɮɢɰɢɟɧɬ ɜɵ-
ɫɨɬɵ 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 ɬɨɥɳɢ-
ɧɚ ɡɭɛɶɟɜ ɤɨɥɟɫ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ Sn1 ɢ Sn2);
ɫɬɟɩɟɧɶ ɬɨɱɧɨɫɬɢ ɩɚɪɵ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɩɨ ɜɫɟɦ ɧɨɪɦɚɦ ɬɨɱɧɨɫɬɢ, ɜɢɞ ɫɨɩɪɹ-
ɠɟɧɢɹ 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 ɞɨ-
ɩɨɥɧɢɬɟɥɶɧɵɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ.
Ⱦɢɚɦɟɬɪɵ ɞɟɥɢɬɟɥɶɧɵɯ ɨɤɪɭɠɧɨɫɬɟɣ
d = |
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cos β |
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ɍɝɨɥ ɩɪɨɮɢɥɹ ɢ ɦɨɞɭɥɶ ɩɨ ɬɨɪɰɭ (ɬɨɪɰɨɜɵɣ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɢ ɬɨɪɰɨ-
ɜɵɣ ɦɨɞɭɥɶ)
d |
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tg α |
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cos β |
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ɞɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ α |
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ɢ m |
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Ⱦɢɚɦɟɬɪɵ ɨɫɧɨɜɧɵɯ ɨɤɪɭɠɧɨɫɬɟɣ |
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d |
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=d cosα |
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b |
= d |
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cosα ; |
( .3) |
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6
ɍɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɜ ɩɟɪɟɞɚɱɟ ɩɨ ɬɨɪɰɭ ɤɨɥɟɫ αtw ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ, ɢɡɜɟɫɬɧɨ ɢɥɢ ɧɟɢɡɜɟɫɬɧɨ ɦɟɠɨɫɟɜɨɟ ɪɚɫɫɬɨɹɧɢɟ αw .
ɉɪɢ ɧɟɡɚɞɚɧɧɨɦ ɦɟɠɨɫɟɜɨɦ ɪɚɫɫɬɨɹɧɢɢ ɞɥɹ ɧɟɤɨɪɪɢɝɢɪɨɜɚɧɧɨɣ ɩɟɪɟɞɚ-
ɱɢ, ɤɨɝɞɚ ɯ1 = 0, ɯ2 = 0 ; αtw =αt ɢ |
y = 0 . |
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Ⱦɥɹ ɤɨɪɪɢɝɢɪɨɜɚɧɧɨɣ ɩɟɪɟɞɚɱɢ αtwɧɚɯɨɞɢɬɫɹ ɩɨɫɥɟ ɨɩɪɟɞɟɥɟɧɢɹ ɢɧɜɨ- |
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ɥɸɬɵ ɭɝɥɚ |
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inv α |
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tg α . |
( .5) |
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z + z2 |
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Ɂɧɚɱɟɧɢɟ |
αtwɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ |
ɪɟɲɟɧɢɹ ɬɪɚɧɫɰɟɧɞɟɧɬɧɨɝɨ |
ɭɪɚɜɧɟɧɢɹ |
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inv α |
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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 α tw = α w
inv α |
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ɉɪɢ |
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ɢɡɜɟɫɬɧɨɦ |
ɦɟɠɨɫɟɜɨɦ |
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ɪɚɫɫɬɨɹɧɢɢ |
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α tw = arccos[( |
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d + d 2 ) cos α t |
2 aw ] . |
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Ɇɟɠɨɫɟɜɨɟ ɪɚɫɫɬɨɹɧɢɟ |
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aw = [0,5m (z + z2 ) cos α t ] (cos α tw cos |
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Ʉɨɷɮɮɢɰɢɟɧɬ ɭɪɚɜɧɢɬɟɥɶɧɨɝɨ ɫɦɟɳɟɧɢɹ y [2,ɫ.75]: |
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y = x |
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Ⱦɥɹ ɤɨɥɟɫ ɛɟɡ ɫɦɟɳɟɧɢɹ x1 = x 2= 0 ; |
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( .6)
ɤɨɥɟɫ
( .7)
( .8)
( .9)
7
Ɋɢɫ. . . Ȼɥɨɤ-ɫɯɟɦɚ ɚɥɝɨɪɢɬɦɚ ɧɚɯɨɠɞɟɧɢɹ ɭɝɥɚ ɩɨ ɡɧɚɱɟɧɢɸ ɟɝɨ ɢɧɜɨɥɸɬɵ ɧɚ ɗȼɆ
8
ȼɵɫɨɬɚ ɝɨɥɨɜɤɢ ɡɭɛɶɟɜ ɤɨɥɟɫ
h |
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= (h |
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( . 0) |
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2(h* + x − y)m ; d |
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+ 2(h* + x − |
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ȼɵɫɨɬɚ ɡɭɛɶɟɜ ɤɨɥɟɫ |
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h = (2h* |
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ɝɞɟ C* - ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɞɢɚɥɶɧɨɝɨ ɡɚɡɨɪɚ (C* = 0,25). |
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ȼɵɫɨɬɚ h ɦɨɠɟɬ ɛɵɬɶɩɨɞɫɱɢɬɚɧɚ ɬɚɤɠɟ ɩɨ ɮɨɪɦɭɥɟ: |
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h = |
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ȼɵɫɨɬɚ ɧɨɠɤɢ ɡɭɛɶɟɜ ɤɨɥɟɫ |
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hf = h – ha ; hf 2 = h – ha 2 . |
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Ⱦɢɚɦɟɬɪ ɜɩɚɞɢɧ ɡɭɛɶɟɜ ɤɨɥɟɫ |
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df1 = da1 -2h ; df2 = da2 -2h. |
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Ɍɨɥɳɢɧɚ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɢ ɫɨɩɪɹɠɟɧɧɨɝɨ ɤɨɥɟɫɚ ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɞɢɚ- |
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ɦɟɬɪɟ (ɟɫɥɢ ɧɟ ɭɤɚɡɚɧɚ ɜ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ) |
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Sn1 |
= 0,5πm + 2 x1 m tgα - ECS1; |
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Sn2 |
= 0,5πm + 2 x2 m tgα - ECS2. |
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ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɲɟɜɟɪɨɜ ɪɚɫɱɟɬɧɵɟ ɡɧɚɱɟɧɢɹ Sn1 ɢ Sn2 ɨɩɪɟɞɟɥɹɸɬ- |
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ɫɹ ɫ ɭɱɟɬɨɦ ɩɨɥɨɜɢɧɵ ɜɟɥɢɱɢɧɵ ɞɨɩɭɫɤɚ ɧɚ ɬɨɥɳɢɧɭɡɭɛɚ: |
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Sn1 |
= 0,5πm + 2 x1 m tgα - ECS1 |
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TC |
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Sn2 |
= 0,5πm + 2 x2 m tgα - ECS2 |
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ɝɞɟ ECS1 ɢ ECS2 - ɧɚɢɦɟɧɶɲɢɟ ɨɬɤɥɨɧɟɧɢɹ ɬɨɥɳɢɧɵ ɡɭɛɚ ɤɨɥɟɫɚ, ɧɟɨɛɯɨ-
ɞɢɦɵɟ 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 S1 ɢ S2. Ⱦɥɹ ɱɚɫɬɢ ɡɭɛɱɚɬɵɯ ɤɨ-
ɥɟɫ ɩɨ ȽɈɋɌ 643-8 [3] ɜɟɥɢɱɢɧɵ ECS ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. . .
Ɍɚɛɥɢɰɚ .
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Ⱦɢɚɦɟɬɪ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ, ɦɦ |
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ȼɢɞ |
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ɫɜ. 80 |
ɫɜ. |
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ɫɜ. |
ɫɜ. |
ɫɜ. |
ɫɜ. |
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ɫɨɩɪɹ- |
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3 5 |
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ɞɨ |
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6 |
0,035 |
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ɇɚɢɛɨɥɶɲɢɣ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ |
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ρ |
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= 0,5 |
d 2 |
− d 2 |
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. 7) |
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Ɋɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɜ ɬɨɱɤɟ ɧɚɱɚɥɚ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ
ρ |
a |
= a |
w |
sinα |
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− 0,5 |
d 2 |
− d 2 |
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a 2 |
b2 . |
. 8) |
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Ⱦɥɢɧɚ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɥɢɧɢɢ ɡɚɰɟɩɥɟɧɢɹ |
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L= 0,5( d2 |
−d2 + |
d2 |
−d2 |
)−a |
sinα . |
( . 9) |
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ɇɟɨɛɯɨɞɢɦɨɟ ɩɪɢ ɲɟɜɢɧɝɨɜɚɧɢɢ ɩɟɪɟɤɪɵɬɢɟ ɨɛɪɚɛɨɬɤɨɣ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ |
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ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ |
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L = 0, 5m sinαtw . |
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ɍɝɨɥ ɧɚɤɥɨɧɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɧɚ ɨɫɧɨɜɧɨɦ ɰɢɥɢɧɞɪɟ ɤɨɥɟɫɚ ɩɨ ɨɬɧɨɲɟ-
ɧɢɸ ɤ ɬɨɪɰɭ (ɞɥɹ ɤɨɫɨɡɭɛɵɯ ɤɨɥɟɫ)
0
σ = arccos(cosα sinβ) . ( .2 )
Ⱦɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ σ = 90° .
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɤɪɵɬɢɹ ɨɛɪɚɛɨɬɤɨɣ ɩɪɢ ɡɚɰɟɩɥɟɧɢɢ ɤɨɥɟɫɚ ɫ ɲɟɜɟɪɨɦ
ε = (L + L) πm (sinσ cosα ) |
( .22) |
Ⱦɨɥɠɧɨ ɛɵɬɶ ε ≥ , . ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɲɟɜɢɧɝɨɜɚɧɢɟ ɧɟɜɨɡɦɨɠɧɨ.
ɢ ɲɟɜɟɪ ɧɟ ɩɪɨɟɤɬɢɪɭɟɬɫɹ.
ȼ ɡɚɞɚɧɢɢ ɧɚ ɤɭɪɫɨɜɨɟ ɢɥɢ ɞɢɩɥɨɦɧɨɟ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɜ ɤɚɱɟɫɬɜɟ ɢɫ-
ɯɨɞɧɵɯ ɞɚɧɧɵɯ ɦɨɝɭɬ ɛɵɬɶ ɭɤɚɡɚɧɵ ɧɨɦɟɪɚ ɱɟɪɬɟɠɟɣ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ, ɦɟɠ-
ɰɟɧɬɪɨɜɨɟ 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 |
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( .23) |
ɝɞɟ p - ɞɢɚɦɟɬɪɚɥɶɧɵɣ ɩɢɬɱ.
Ɉɤɪɭɠɧɨɣ ɩɢɬɱ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɲɚɝ ɦɟɠɞɭɡɭɛɶɹɦɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ
ɨɤɪɭɠɧɨɫɬɢ, ɜɵɪɚɠɟɧɧɵɣ ɜ ɞɸɣɦɚɯ. Ɇɟɠɞɭ ɨɤɪɭɠɧɵɦ ɩɢɬɱɟɦ P, ɞɢɚɦɟɬ-
ɪɚɥɶɧɵɦ 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) ɫɢɫ-
ɬɟɦɚ ɡɚɰɟɩɥɟɧɢɹ, ɧɚɩɪɢɦɟɪ m1/m2. ȼ ɷɬɨɣ ɫɢɫɬɟɦɟ ɪɚɡɦɟɪɵ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤ-
ɪɭɠɧɨɫɬɢ ɢ ɬɨɥɳɢɧɵ ɡɭɛɶɟɜ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɩɨ ɛɨɥɶɲɨɦɭ ɦɨɞɭɥɸ, ɚ ɜɵɫɨɬɵ ɡɭɛɶɟɜ - ɩɨ ɦɚɥɨɦɭ ɦɨɞɭɥɸ, ɬ.ɟ. ɤɨɥɟɫɚ ɢɦɟɸɬ ɭɤɨɪɨɱɟɧɧɭɸ ɩɪɨɬɢɜ ɨɛɵɱɧɨɣ ɜɵɫɨɬɭɡɭɛɶɟɜ.
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 ɮɨɪ-
ɦɭɥɚɦ:
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Sn = d cos β arcsin ( Sx /(d cos β). |
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ɇɚ ɱɟɪɬɟɠɟ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ ɦɨɠɟɬ ɛɵɬɶ ɭɤɚɡɚɧ ɪɚɡɦɟɪ Ʉ ɩɨ ɪɨɥɢɤɚɦ
(ɲɚɪɢɤɚɦ) ɞɢɚɦɟɬɪɚ dɒ. Ɍɨɝɞɚ ɞɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ ɫ ɱɟɬɧɵɦ ɱɢɫɥɨɦ ɡɭɛɶ-
ɟɜ ɬɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɞɭɝɟ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɦɨɠɟɬ ɛɵɬɶ ɩɨɞɫɱɢɬɚɧɚ ɩɨ ɮɨɪɦɭɥɚɦ:
M = |
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Sn = d ( |
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Ⱦɥɹ ɧɟɱɟɬɧɨɝɨ ɱɢɫɥɚ ɡɭɛɶɟɜ ɤɨɥɟɫɚ ɪɚɡɦɟɪ
K −dɒ
M = 2cos π ;
2z
ɚɜɟɥɢɱɢɧɵ αD ɢ Sn ɩɨɞɫɱɢɬɵɜɚɸɬɫɹ ɬɚɤ ɠɟ, ɩɨ ɮɨɪɦɭɥɚɦ ( .26).
( .26)
( .27)
Ⱦɥɹ ɤɨɫɨɡɭɛɵɯ ɤɨɥɟɫ ɪɚɡɦɟɪ Ɇ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɞɥɹ ɩɪɹɦɨɡɭ-
ɛɵɯ, ɬ.ɟ. ɩɨ ɮɨɪɦɭɥɚɦ:
M = |
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M = |
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2cos |
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Ɂɞɟɫɶ ɜɟɥɢɱɢɧɚ Ʉ - ɨɯɜɚɬɵɜɚɸɳɢɣ ɪɚɡɦɟɪ ɩɨ ɲɚɪɢɤɚɦ.
Ɍɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɧɨɪɦɚɥɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɫɨɡɭɛɨɝɨ ɤɨɥɟ-
ɫɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ:
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ó = arccos[cos (arctg |
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Ɋɚɫɱɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɲɥɢɰɟɜɵɯ ɜɚɥɨɜ ɫ ɷɜɨɥɶɜɟɧɬɧɵɦɢ ɡɭɛɶɹɦɢ ɧɟ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɪɚɫɱɟɬɚ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɱɚɬɵɯ ɤɨ-
ɥɟɫ. Ɉɫɨɛɟɧɧɨɫɬɶɸ ɪɚɫɱɟɬɚ ɡɭɛɨɪɟɡɧɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ (ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ, ɞɨɥ-
ɛɹɤɨɜ) ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɹɜɥɹɟɬɫɹ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ ɞɢɚɦɟɬɪɚ ɨɤɪɭɠ-
ɧɨɫɬɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɧɚɱɚɥɭɪɚɛɨɱɟɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɜɚɥɚ dp .
ȿɫɥɢ ɷɬɨɬ ɞɢɚɦɟɬɪ ɧɚ ɱɟɪɬɟɠɟ ɧɟ ɭɤɚɡɚɧ, ɬɨ ɫɥɟɞɭɟɬ ɨɛɪɚɬɢɬɶɫɹ ɤ ɫɬɚɧ-
ɞɚɪɬɭɧɚ ɲɥɢɰɟɜɵɟ ɫɨɟɞɢɧɟɧɢɹ ɋɌ ɋɗȼ 268-76 [4].
Ⱥ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɜ ɬɨɱɤɟ ɧɚɱɚɥɚ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɜɚɥɚ ɪɚɫɫɱɢɬɚɬɶ ɩɨ ɮɨɪɦɭɥɟ:
ρ P = |
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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 ɜɚɪɢɚɧ-
ɬɵ 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