Кафедра ДМ 09 04 2013 / Киреев - Расчёт И Проектирование Зуборезных Инструментов
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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 ɡɧɚɱɟ-
ɧɢɟ ɭɝɥɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ αw0 ɧɚ ° ɢ, ɧɚɱɢɧɚɹ ɫ ɮɨɪɦɭɥɵ (2.34), ɩɪɨɢɡɜɟ-
ɫɬɢ ɩɟɪɟɪɚɫɱɟɬ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɶɟɜ ɮɪɟɡɵ. ɍɦɟɧɶɲɟɧɢɟ ɭɝɥɚ ɩɪɨɮɢɥɹ αw0
ɦɨɠɧɨ ɩɪɨɢɡɜɨɞɢɬɶ ɞɨ ɡɧɚɱɟɧɢɹ
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αw0 ≥ αw0 min . |
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Ɇɨɠɧɨ ɬɚɤɠɟ ɢ ɭɦɟɧɶɲɢɬɶ r2.
Ɉɬɫɭɬɫɬɜɢɟ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɩɪɨɮɢɥɟɣ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ ɜ ɡɚɰɟɩɥɟɧɢɢ ɬɚɤ-
ɠɟ ɜɵɪɚɠɚɟɬɫɹ ɭɫɥɨɜɢɟɦ:
rp > rp′ . |
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Ɋɚɫɱɟɬ rp |
ɢ rp′ ɜɵɩɨɥɧɹɟɬɫɹ ɩɨ ɬɟɦ ɠɟ, ɱɬɨ ɢ ɞɥɹ ɩɨɞɪɟɡɚ ɩɪɨɮɢɥɹ ɡɭɛɚ |
ɤɨɥɟɫɚ, ɮɨɪɦɭɥɚɦ. ɇɚɢɛɨɥɟɟ ɩɪɨɫɬɨ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ 2.55, ɟɫɥɢ ɭɦɟɧɶ-
ɲɢɬɶ ɜɟɥɢɱɢɧɭ rz ɞɨ ɟɝɨ ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɨɝɨ ɡɧɚɱɟɧɢɹ.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɚɫɱɟɬɨɜ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɨɩɬɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɫɥɟɞɭɸ-
ɳɢɯ 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 ɩɚ-
ɪɚɦɟɬɪɨɜ ɮɪɟɡɵ ɩɪɨɢɡɜɨɞɢɬɶ ɩɨ ɮɨɪɦɭɥɚɦ ɢ ɬɚɛɥɢɰɚɦ ɪɚɡɞɟɥɚ 2 ɢ ɩɨɞɪɚɡɞɟ-
ɥɚ 2. , ɫɥɟɞɭɟɬ ɨɩɪɟɞɟɥɢɬɶ ɫɥɟɞɭɸɳɢɟ ɜɟɥɢɱɢɧɵ.
Ɍɨɥɳɢɧɭ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɣ ɩɪɹɦɨɣ
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ɉɪɢ αw0 =α, |
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Ⱦɢɚɦɟɬɪ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɮɪɟɡɵ ɜ ɪɚɫɱɟɬɧɨɦ ɫɟɱɟɧɢɢ
Dw =Dt - 2 hn0. (2.57)
ɍɝɨɥɧɚɤɥɨɧɚ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢɱɟɪɜɹɱɧɨɣɧɚɪɟɡɤɢɧɚ ɧɚɱɚɥɶɧɨɦɰɢɥɢɧɞɪɟ
ω = arctg |
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Ɉɫɟɜɨɣ ɲɚɝ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɮɪɟɡɵ
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ɉɪɢ αw0 =α , Px0 = |
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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 ɩɪɢɜ = |
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z2 |
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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 ɡɚ-
ɬɵɥɤɚ ɨɫɧɨɜɧɨɝɨ ɡɚɬɵɥɨɜɚɧɢɹ Ʉ, ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɡɚɬɵɥɨɜɚɧɢɹ Ʉ1 ɩɪɨɢɡɜɨ-
ɞɢɬɫɹ ɩɨ ɨɛɳɟɩɪɢɧɹɬɨɣ ɦɟɬɨɞɢɤɟ, ɢɡɥɨɠɟɧɧɨɣ ɧɚ ɫ. 6–20. Ɂɧɚɱɢɬɟɥɶɧɨ ɨɬ-
ɥɢɱɚɟɬɫɹ ɪɚɫɱɟɬ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɮɪɟɡɵ.
ɇɚ ɪɢɫ.2.4 ɩɪɟɞɫɬɚɜɥɟɧɵ ɜɚɪɢɚɧɬɵ ɦɨɞɢɮɢɤɚɰɢɢ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɱɟɪ-
ɜɹɱɧɵɯ ɮɪɟɡ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɢɦ ɩɪɨɮɢɥɢ ɨɛɪɚɛɨɬɚɧ-
ɧɵɯ ɡɭɛɶɟɜ ɤɨɥɟɫ [ 0].
– Ⱦɥɹ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ m = ÷2 ɦɦ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɧɢɦɚɬɶ ɮɨɪɦɭȺ.
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Ⱦɥɹ ɷɬɨɣ ɮɨɪɦɵ Įw0 = 8°40' – 9° ɩɪɢ Į = 20° .
–Ⱦɥɹ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ m = 2÷ 2 ɦɦ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɧɢɦɚɬɶ ɮɨɪɦɭȼ.
–Ⱦɥɹ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ m = ÷6 ɦɦ ɢɧɨɝɞɚ ɦɨɠɧɨ ɩɪɢɧɢɦɚɬɶ ɮɨɪɦɭȻ.
Ⱦɚɥɶɧɟɣɲɢɣ ɪɚɫɱɟɬ ɩɚɪɚɦɟɬɪɨɜ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɮɪɟɡɵ ɨɬɧɨɫɢɬɫɹ ɤ ɮɨɪ-
ɦɟ ȼ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɣ ɧɚɢɥɭɱɲɢɟ ɭɫɥɨɜɢɹ ɲɟɜɢɧɝɨɜɚɧɢɹ ɡɭɛɶɟɜ ɤɨɥɟɫ.
Ɋɢɫ. 2.4. Ɏɨɪɦɚ ɡɭɛɶɟɜ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ – ɚ)
ɢɮɨɪɦɚ ɡɭɛɶɟɜ ɤɨɥɟɫ, ɨɛɪɚɛɨɬɚɧɧɵɯ ɷɬɢɦɢ ɮɪɟɡɚɦɢ – ɛ)
ȼɬɚɛɥ. 2.5 ɩɪɢɜɟɞɟɧɵ ɭɝɥɵ ɩɪɨɮɢɥɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɫɥɨɜɢɣ ɢɫɩɨɥɶ-
ɡɨɜɚɧɢɹ ɢɧɫɬɪɭɦɟɧɬɚ ɢ ɩɨɜɬɨɪɧɚɹ ɢɧɮɨɪɦɚɰɢɹ ɩɨ ɜɵɛɨɪɭ ɱɢɫɥɚ ɡɚɯɨɞɨɜ
ɮɪɟɡɵ i.
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Ɍɚɛɥɢɰɚ 2.5. |
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ɍɫɥɨɜɢɹ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɧɫɬɪɭɦɟɧɬɚ |
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ɉɪɟɢɦɭɳɟ- |
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ɉɪɢɦɟɧɟɧɢɟ ɜ ɭɫɥɨɜɢɹɯ |
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ɫɬɜɟɧɧɨɟ |
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ɉɚɪɚɦɟɬɪɵ ɤɨɥɟɫɚ |
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ɩɪɢɦɟɧɟɧɢɟ |
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ɦɚɫɫɨɜɨɝɨ ɩɪɨɢɡɜɨɞɫɬɜɚ |
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ɢ ɢɧɫɬɪɭɦɟɧɬɚ |
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Ⱦɥɹ ɧɟɱɺɬɧɨ- |
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Ⱦɥɹ ɱɺɬ- |
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Ⱦɥɹ ɥɸɛɨɝɨ |
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ɝɨ ɱɢɫɥɚ |
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ɧɨɝɨ ɱɢɫɥɚ |
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ɱɢɫɥɚ ɡɭɛɶɟɜ |
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ɡɭɛɶɟɜ ɤɨɥɟ- |
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ɡɭɛɶɟɜ ɤɨ- |
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ɫɚ |
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ɑɢɫɥɨ ɡɚɯɨɞɨɜ ɮɪɟɡɵ i |
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ɉɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɤɨɥɟɫɚ |
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20° |
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5° |
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ɉɪɨɮɢɥɶɧɵɣ ɭɝɨɥ ɮɪɟɡɵ ɜ ɧɨɪ- |
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ɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ |
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ɉɪɢ df1 < db1 ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ ɧɚɢɦɟɧɶɲɢɣ ɩɪɨɮɢɥɶɧɵɣ ɭɝɨɥ |
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ɡɭɛɶɟɜ ɮɪɟɡɵ, ɝɚɪɚɧɬɢɪɭɸɳɢɣ ɨɬɫɭɬɫɬɜɢɟ ɩɨɞɪɟɡɚɧɢɹ ɡɭɛɚ ɤɨɥɟɫɚ. |
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α w0 min |
= arccos |
d f |
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(2.62) |
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ȿɫɥɢ ɩɨɞɪɟɡɤɚ ɡɭɛɚ ɤɨɥɟɫɚ ɧɟ ɞɨɩɭɫɤɚɟɬɫɹ, |
ɬɨ ɞɨɥɠɧɨ ɛɵɬɶ ɜɵɞɟɪɠɚɧɨ |
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ɭɫɥɨɜɢɟ: |
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α |
≥ α w min. |
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(2.63) |
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Ɇɨɠɧɨ ɩɪɢɧɹɬɶ α w |
= α w |
min . |
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(2.64) |
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Ɋɢɫ. 2.5. Ɋɚɡɦɟɪɵ ɡɭɛɶɟɜ ɮɨɪɦɵ ȼ - ɚ) ɢ ɜɚɪɢɚɧɬ ɨɮɨɪɦɥɟɧɢɹ ɭɫɢɤɚ - ɛ)
38
ɉɪɢɩɭɫɤ ɩɨɞ ɲɟɜɢɧɝɨɜɚɧɢɟ ɫɥɟɞɭɟɬ ɩɪɢɧɹɬɶ ɢɡ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɪɨ-
ɰɟɫɫɚ ɢɡɝɨɬɨɜɥɟɧɢɹ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ ɢɥɢ ɪɚɫɫɱɢɬɚɬɶ ɩɨ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɟ:
ǻS = 0,0 7 m + 0,08. (2.65)
Ɂɧɚɱɟɧɢɟ ǻS ɨɤɪɭɝɥɢɬɶ ɞɨ ɫɨɬɵɯ ɞɨɥɟɣ ɦɢɥɥɢɦɟɬɪɚ ɜ ɛɨɥɶɲɭɸ ɫɬɨɪɨɧɭ.
ɉɪɢɩɭɫɤ ɧɚ ɫɬɨɪɨɧɭɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ
δ = S . 2
Ɉɫɧɨɜɧɨɣ ɲɚɝ ɤɨɥɟɫɚ ɢ ɮɪɟɡɵ
Pb = π m cosα .
ɒɚɝ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ
Pw 0 |
= |
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cos |
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ɍɝɨɥ ɧɚɤɥɨɧɚ ɡɭɛɚ ɤɨɥɟɫɚ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ
β w |
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sin β cos α |
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cos α w |
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ɍɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɮɪɟɡɵ ɢ ɤɨɥɟɫɚ ɜ ɬɨɪɰɨɜɨɣ ɩɥɨɫɤɨɫɬɢ ɤɨɥɟɫɚ
α |
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tg α w |
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cos β w |
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(2.66)
(2.67)
(2.68)
(2.69)
(2.70)
Ⱦɢɚɦɟɬɪ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟɫɚ
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d cos α |
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d w |
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(2.7 ) |
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cos |
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Ɍɨɥɳɢɧɚ ɡɭɛɚ ɩɨ ɧɨɪɦɚɥɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟɫɚ |
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S |
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+ inv α |
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− inv α |
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α wt |
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d |
cos |
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Ɋɚɫɱɟɬɧɵɟ ɪɚɡɦɟɪɵ ɡɭɛɚ ɮɪɟɡɵ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ:
– ɬɨɥɳɢɧɚ ɡɭɛɚ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ɮɪɟɡɵ |
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S |
n 0 |
= P |
w 0 |
− S |
w |
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(2.73) |
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39
–ɜɵɫɨɬɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɨɬ ɟɝɨ ɜɟɪɲɢɧɵ ɞɨ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ
(ɪɢɫ. 2.6)
hn |
= |
d w − d |
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(2.74) |
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- ɜɵɫɨɬɚ ɡɭɛɚ ɮɪɟɡɵ |
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h0 = h + 0,3m . |
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Ɋɢɫ.2.6. Ɉɩɪɟɞɟɥɟɧɢɟ ɪɚɡɦɟɪɨɜ ɭɫɢɤɨɜ ɡɭɛɚ ɩɪɹɦɨɣ ɮɪɟɡɵ
ɜ ɬɨɪɰɨɜɨɣ ɩɥɨɫɤɨɫɬɢ ɤɨɥɟɫɚ
Ɋɚɫɫɬɨɹɧɢɟ ɨɬ ɜɟɪɲɢɧɵ ɡɭɛɚ ɮɪɟɡɵ ɞɨ ɧɚɱɚɥɚ ɭɬɨɥɳɟɧɢɹ (ɪɢɫ.2.6)
h |
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0,5d |
sin α |
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Ɋɚɡɦɟɪɵ ɭɫɢɤɚ ɡɭɛɚ, ɩɪɨɫɬɚɜɥɹɟɦɵɟ ɧɚ ɱɟɪɬɟɠɟ (ɪɢɫ.2.5), ɫɥɟɞɭɸɳɢɟ:
c = |
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a = δ + 0,05; |
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cosα w |
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b = c − |
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− sin α w0 |
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40
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 ɱɪɟɡɦɟɪ-
ɧɨɝɨ ɩɨɞɪɟɡɚɧɢɹ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ. Ⱦɥɹ ɷɬɨɝɨ ɧɚ ɨɫɧɨɜɚɧɢɢ ɪɢɫ.2.7 ɫɥɟɞɭɟɬ ɩɪɨɢɡɜɟɫɬɢ ɫɥɟɞɭɸɳɢɟ ɪɚɫɱɟɬɵ:
- ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ ɞɨ ɬɨɱɤɢ, ɩɪɨɢɡɜɨɞɹɳɟɣ ɧɚɢɛɨɥɶ-
ɲɭɸ ɩɨɞɪɟɡɤɭ
h |
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- ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ ɧɚɱɚɥɚ ɚɤɬɢɜɧɨɝɨ ɭɱɚɫɬɤɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ |
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r |
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(2.79) |
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- ɭɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ ɜ ɬɨɱɤɟ ȼ |
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αȼ = arccos |
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b |
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-ɭɝɨɥ Ȝ (ɫɦ. ɪɢɫ.2.7)
λ= arccos 0,5dw − hk ; rȼ
-ɭɝɨɥ ij (ɪɢɫ.2.7)
ϕ = λ + invαwt0 − invα |
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- ɜɟɥɢɱɢɧɭ lt (ɪɢɫ.2.7)
ɟ |
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tgα |
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- ɪɚɡɦɟɪ l (ɧɚ ɪɢɫ.2.7 ɧɟ ɩɨɤɚɡɚɧ) |
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e |
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cos |
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cos |
β w . |
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(2.82)
(2.83)
4
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 ɢɡɝɨ-
ɬɨɜɥɟɧɢɹ 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: |
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hf = 0,075·m + 0,35; |
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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 |
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+ 0°. |
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Ⱦɢɚɦɟɬɪ ɨɤɪɭɠɧɨɫɬɢ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ, ɫ ɤɨɬɨɪɨɣ ɧɚɱɢɧɚɟɬɫɹ ɮɥɚɧɤ |
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d A |
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ɍɝɨɥ ɩɪɨɮɢɥɹ ɧɚ ɞɢɚɦɟɬɪɟ dA ɞɥɹ ɨɫɧɨɜɧɨɣ ɷɜɨɥɶɜɟɧɬɵ |
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dw |
cosα w |
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α |
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ɍɝɨɥ ɩɪɨɮɢɥɹ ɧɚ ɞɢɚɦɟɬɪɟ dA ɞɥɹ ɷɜɨɥɶɜɟɧɬɵ ɮɥɚɧɤɚ |
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dw |
cosαɮ |
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αɮȺ = arccos |
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0 |
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(2.88) |
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d A |
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43