Кафедра ДМ 09 04 2013 / Киреев - Расчёт И Проектирование Зуборезных Инструментов
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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 ɞɥɢɧɵɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɡɭɛɚɮɪɟɡɵ 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. |
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arctg (tgαɜ sinαw0 ) ≥ ( ,5÷2)°. |
(2. 8) |
ɋ ɩɨɦɨɳɶɸ ɗȼɆ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɞɨɫɬɚɬɨɱɧɨɫɬɶ ɩɪɨɲɥɢɮɨɜɚɧɧɨɣ |
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ɱɚɫɬɢ ɡɭɛɶɟɜ ɮɪɟɡɵ ɧɚ ɨɫɧɨɜɟ ɚɧɚɥɢɬɢɱɟɫɤɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ [8]. |
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ɋɪɟɞɧɢɣ ɪɚɫɱɟɬɧɵɣ ɞɢɚɦɟɬɪ ɮɪɟɡɵ |
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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 ɰɢ-
ɥɢɧɞɪɟ
ω t = arcsin(m i /Dt ). |
(2.20) |
Ɂɧɚɱɟɧɢɟ ωt ɩɨɞɫɱɢɬɵɜɚɟɬɫɹ ɫ ɬɨɱɧɨɫɬɶɸ ″ .
ɇɚɩɪɚɜɥɟɧɢɟ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɩɪɚɜɨɟ, ɟɫɥɢ ɩɪɨɟɤɬɢ-
ɪɭɟɬɫɹ ɮɪɟɡɚ ɞɥɹ ɩɪɹɦɨɡɭɛɵɯ ɤɨɥɟɫ ɢɥɢ ɤɨɫɨɡɭɛɵɯ ɤɨɥɟɫ ɫ ɩɪɚɜɵɦ ɧɚɩɪɚɜɥɟ-
ɧɢɟɦ ɡɭɛɶɟɜ. Ⱦɥɹ ɤɨɫɨɡɭɛɵɯ ɤɨɥɟɫ ɫ ɥɟɜɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɡɭɛɶɟɜ ɩɪɨɟɤɬɢɪɭ-
ɟɬɫɹ 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 ɧɚ-
ɩɪɚɜɥɟɧɢɸ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ.
ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɦɨɠɧɨ ɩɪɨɟɤɬɢɪɨɜɚɬɶ ɱɟɪɜɹɱɧɵɟ ɮɪɟɡɵ ɫ wt ≤ 3° ɫ ɩɪɹɦɵ-
ɦɢ ɫɬɪɭɠɟɱɧɵɦɢ ɤɚɧɚɜɤɚɦɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɦɢ ɜɞɨɥɶ ɨɫɢ ɮɪɟɡɵ, ɬ.ɟ. wk = 0°.
ɒɚɝ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ
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π Dt |
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Ρz |
= tgω |
; ɞɥɹ ωk= 0° − Pz = ∞. |
(2.2 ) |
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k |
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ɒɚɝ ɜɢɬɤɨɜ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ ɩɨ ɨɫɢ ɮɪɟɡɵ |
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Ρx0 |
= |
Ρt0 i |
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(2.22) |
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cosωt |
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ɍɝɨɥ ɭɫɬɚɧɨɜɤɢ ɮɪɟɡɵ ɧɚ ɫɬɚɧɤɟ |
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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 ɱɟɪɜɹɱɧɨɣɮɪɟɡɵ (ɩɨɞɞɚɥɶɧɟɣɲɭɸɱɢɫɬɨɜɭɸɨɛɪɚɛɨɬɤɭ ɢɥɢ ɞɥɹɧɢɡɤɢɯ ɫɬɟɩɟɧɟɣ ɬɨɱɧɨɫɬɢɡɭɛɱɚɬɵɯ ɤɨɥɟɫ) - ɬɨɥɶɤɨɩɪɨɮɢɥɶɡɭɛɶɟɜɜɧɨɪɦɚɥɶɧɨɦɫɟɱɟɧɢɢ.
ɍɝɨɥ ɩɪɨɮɢɥɹ ɜ ɨɫɟɜɨɦ ɫɟɱɟɧɢɢ ɨɫɧɨɜɧɨɝɨ ɚɪɯɢɦɟɞɨɜɚ ɱɟɪɜɹɤɚ
αɈɋ = arctg |
tgα w0 |
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(2.24) |
cosω |
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t |
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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 |
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Pz |
tgαɈɋ |
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P |
#ɤ |
z |
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tgα |
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0 |
Ɉɋ |
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z |
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α xL0 |
= arctg |
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Pz |
tgαɈɋ |
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(2.25) |
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± ɤ z0 tgαɈɋ |
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ȼ ɮɨɪɦɭɥɚɯ ɜɟɪɯɧɢɟ ɡɧɚɤɢ ( «-», «+» ) ɨɬɧɨɫɹɬɫɹ ɤ ɩɪɚɜɨɡɚɯɨɞɧɵɦ ɮɪɟ-
ɡɚɦ, ɧɢɠɧɢɟ («+», «-»)- ɤ ɥɟɜɨɡɚɯɨɞɧɵɦ. ɉɪɢ wk= 0°, αxR0=αxL0= =αɈɋ .
Ɉɫɟɜɨɣ ɲɚɝ ɡɭɛɶɟɜ ɮɪɟɡɵ
PɈɋ.O = |
Pto |
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cosω |
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(2.26) |
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t |
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Ɍɨɥɳɢɧɚ ɡɭɛɶɟɜ ɮɪɟɡɵ ɜ ɨɫɟɜɨɦ ɫɟɱɟɧɢɢ ɧɚ ɞɟɥɢɬɟɥɶɧɨɦ ɞɢɚɦɟɬɪɟ |
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SɈɋ.O |
= |
Sto |
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(2.27) |
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cosω |
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t |
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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 |
d1, ɦɦ |
l, ɦɦ |
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7 |
50 |
5 |
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80 |
55 |
~ “ ~ |
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90 |
60 |
~ “ ~ |
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00 |
65 |
~ “ ~ |
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2 |
70 |
~ “ ~ |
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25 |
80 |
~ “ ~ |
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40 |
85 |
~ “ ~ |
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60 |
90 |
~ “ ~ |
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80 |
95 |
~ “ ~ |
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200 |
00 |
~ “ ~ |
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225 |
20 |
~ “ ~ |
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Ɍɚɛɥɢɰɚ 2.3 |
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dao, ɦɦ |
d1, ɦɦ |
l, ɦɦ |
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40 |
26 |
4 |
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50 |
33 |
~ “ ~ |
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63-7 |
40 |
~ “ ~ |
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8000 |
50 |
~ “ ~ |
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2- 40 |
60 |
5 |
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6080 |
75 |
5 |
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ɉɪɟɠɞɟ ɱɟɦ ɨɩɪɟɞɟɥɢɬɶ ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɭɸ ɞɥɢɧɭ ɪɚɛɨɱɟɣ ɱɚɫɬɢ
LP , ɢɫɯɨɞɹ ɢɡ ɞɥɢɧɵ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɥɢɧɢɢ ɡɚɰɟɩɥɟɧɢɹ ɮɪɟɡɵ ɢ ɤɨɥɟɫɚ, ɧɟɨɛ-
ɯɨɞɢɦɨ ɪɚɫɫɱɢɬɚɬɶ:
- ɭɝɨɥ ɞɚɜɥɟɧɢɹ (ɩɪɨɮɢɥɹ) ɧɚ ɝɨɥɨɜɤɟ ɡɭɛɚ ɤɨɥɟɫɚ
α |
= arccos |
db |
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a |
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da |
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- ɭɝɨɥ ɡɚɰɟɩɥɟɧɢɹ ɮɪɟɡɵ ɢ ɤɨɥɟɫɚ ɜ ɬɨɪɰɨɜɨɦ ɫɟɱɟɧɢɢ ɤɨɥɟɫɚ
α wt0 |
= arctg |
tgα w0 |
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cosβ |
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Ɇɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɚɹ ɞɥɢɧɚ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɮɪɟɡɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ
ɮɨɪɦɭɥɟ:
L |
= |
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sin α |
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−d sin α |
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cos ψ |
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cos β+2POC.O (2.28) |
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d |
a |
ω |
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cos α |
ωt0 |
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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.
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Ɍɚɛɥɢɰɚ 2.4. |
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ɇɨɦɢ- |
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Ɋɚɡɦɟɪ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ |
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Ⱦɨɩɭɫ- |
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ɧɚɥɶɧɵɣ |
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ȼɵɫɨɬɚ ɩɚɡɚ ɨɬ |
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ɤɚɟɦɨɟ |
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ɞɢɚɦɟɬɪ |
ɒɢɪɢɧɚ ɩɚɡɚ bn, |
ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɣ |
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Ɋɚɞɢɭɫ ɡɚ- |
ɫɦɟɳɟ- |
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ɨɬɜɟɪɫɬɢɹ |
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ɫɬɨɪɨɧɵ ɨɬɜɟɪ- |
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ɧɢɟ ɩɚɡɚ |
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ɦɦ |
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ɮɪɟɡɵ, |
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ɫɬɢɹ ɋ , ɦɦ |
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ɤɪɭɝɥɟɧɢɹ ɜ |
ɨɬɧɨɫɢ- |
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dɨɬɜ, ɦɦ |
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ɩɚɡɭ R, ɦɦ |
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ɇɨɦɢ- |
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Ⱦɨɩɭɫɤ |
ɇɨɦɢ- |
Ⱦɨɩɭɫɤ |
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ɬɟɥɶɧɨ |
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ɧɚɥ |
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ɧɚɥ |
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ɨɫɢ ɨɬɜ. |
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6 |
4 |
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ɋ |
7,7 |
ɇ 2 |
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0,4+0,2 |
0,07 |
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22 |
6 |
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ɋ |
24 |
ɇ 2 |
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0,7+0,3 |
0,09 |
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27 |
7 |
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ɋ |
29,8 |
ɇ 2 |
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0,9+0,3 |
0,09 |
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32 |
8 |
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ɋ |
34,8 |
ɇ 2 |
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0,9+0,3 |
0,09 |
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40 |
0 |
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ɋ |
43,5 |
ɇ 2 |
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0,9+0,3 |
0,09 |
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50 |
2 |
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ɋ |
53,5 |
ɇ 2 |
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+0,5 |
0, 2 |
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60 |
4 |
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ɋ |
64,2 |
ɇ 2 |
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, +0,5 |
0, 2 |
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ɉɨ ɬɪɟɛɨɜɚɧɢɸ ɡɚɤɚɡɱɢɤɚ ɭ ɱɟɪɜɹɱɧɵɯ ɮɪɟɡ ɞɥɹ ɨɛɪɚɛɨɬɤɢ |
ɤɨɫɨɡɭɛɵɯ |
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ɤɨɥɟɫ β >20° ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹ ɡɚɛɨɪɧɵɣ ɤɨɧɭɫ ɫ ɩɚɪɚɦɟɬɪɚɦɢ: |
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ɞɥɢɧɚ ɤɨɧɭɫɚ lɄ = 6 m; |
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ɭɝɨɥ ɤɨɧɭɫɚ ϕɄ = 8° . |
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(2.29) |
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Ⱦɥɢɧɚ ɲɥɢɮɨɜɚɧɧɨɣ ɱɚɫɬɢ ɨɬɜɟɪɫɬɢɹ ɮɪɟɡɵ |
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lɲ = 0,3 L . |
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Ⱦɢɚɦɟɬɪ ɜɵɬɨɱɤɢ ɜ ɨɬɜɟɪɫɬɢɢ |
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dɜ = dɨɬɜ+ 2 |
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ɉɨɫɥɟ ɜɫɟɯ ɪɚɫɱɟɬɨɜ ɫɥɟɞɭɟɬ ɩɪɨɜɟɪɢɬɶ ɭɫɥɨɜɢɹ: |
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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 ɱɢɫ-
ɬɨɜɨɣ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɩɪɹɦɨɡɭɛɨɝɨ ɤɨɥɟɫɚ
ȼ ɤɚɱɟɫɬɜɟ ɤɪɢɬɟɪɢɹ ɨɩɬɢɦɢɡɚɰɢɢ ɩɪɢɧɹɬɨ ɩɨɜɵɲɟɧɢɟ ɩɟɪɢɨɞɚ ɫɬɨɣɤɨ-
ɫɬɢ ɢɧɫɬɪɭɦɟɧɬɚ, ɡɚɜɢɫɹɳɟɝɨ ɨɬ ɜɟɥɢɱɢɧɵ ɡɚɞɧɟɝɨ ɭɝɥɚ ɜ ɦɟɫɬɟ ɫɨɩɪɹɠɟɧɢɹ ɛɨɤɨɜɨɣ ɢ ɜɟɪɲɢɧɨɣ ɪɟɠɭɳɢɯ ɤɪɨɦɨɤ. Ɉɝɪɚɧɢɱɟɧɢɟɦ ɫɥɭɠɢɬ ɬɪɟɛɭɟɦɨɟ ɤɚ-
ɱɟɫɬɜɨ ɡɭɛɱɚɬɵɯ ɤɨɥɟɫ, ɧɚɪɟɡɚɟɦɵɯ ɫ ɩɨɦɨɳɶɸ ɷɬɨɝɨ ɢɧɫɬɪɭɦɟɧɬɚ: ɨɬɫɭɬɫɬ-
ɜɢɟ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɩɪɨɮɢɥɟɣ ɡɭɛɶɟɜ ɡɚɰɟɩɥɹɸɳɢɯɫɹ ɤɨɥɟɫ, ɢ, ɟɫɥɢ ɬɪɟɛɭɟɬ-
ɫɹ, ɬɨ ɨɬɫɭɬɫɬɜɢɟ ɩɨɞɪɟɡɤɢ ɩɪɨɮɢɥɹ ɭɨɫɧɨɜɚɧɢɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ.
Ɇɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɭɝɨɥ ɩɪɨɮɢɥɹ ɡɭɛɚ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɢɡ ɭɫɥɨ-
ɜɢɹ ɦɢɧɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɨɝɨ ɡɚɞɧɟɝɨ ɭɝɥɚ ɧɚ ɛɨɤɨɜɨɣ ɪɟɠɭɳɟɣ ɤɪɨɦɤɟ
α |
ωomin |
= arcsin |
tgαɛɨɤ |
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(2.32) |
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tgαɜ |
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ɝɞɟ αɛɨɤ - ɡɚɞɧɢɣ ɭɝɨɥ ɧɚ ɛɨɤɨɜɨɣ ɪɟɠɭɳɟɣ ɤɪɨɦɤɟ. |
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Ɋɟɤɨɦɟɧɞɭɟɬɫɹ αɛɨɤ = 2°30' ÷3°, |
αɜ = 9°÷12° . |
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29
ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɩɪɢɧɢɦɚɸɬɫɹ ɡɧɚɱɟɧɢɹ ɭɝɥɚ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɪɟɣɤɢ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ αω0 ɢ ɪɚɞɢɭɫ ɫɨɩɪɹɠɟɧɢɹ ɛɨɤɨɜɨɣ ɢ ɜɟɪɲɢɧɧɨɣ ɪɟɠɭ-
ɳɢɯ ɤɪɨɦɨɤ ɪɚɜɧɵɦɢ: |
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αω0=α; rɝ = 0,2 m. |
(2.33) |
Ɍɨɝɞɚ ɪɚɞɢɭɫ ɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ ɩɪɢ ɡɚɰɟɩɥɟɧɢɢ |
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ɟɝɨ ɫ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɨɣ ɫ ɭɝɥɨɦ ɩɪɨɮɢɥɹ αω0 (ɪɢɫ.2.2) |
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rw1 = 0,5 d1 cos α / cosαω0. |
(2.34) |
ȼɵɫɨɬɚ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ ɨɬ ɜɟɪɲɢɧɵ ɡɭɛɶɟɜ ɞɨ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ |
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hn0 = rw1 - 0,5 df1. |
(2.35) |
ɇɚ ɪɢɫ.2.2 ɫɢɦɜɨɥɵ ɨɛɨɡɧɚɱɚɸɬ ɫɥɟɞɭɸɳɟɟ: |
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rz - ɪɚɞɢɭɫ ɫɨɩɪɹɠɟɧɢɹ ɛɨɤɨɜɨɣ ɢ ɜɟɪɲɢɧɧɨɣ ɪɟɠɭɳɢɯ ɤɪɨɦɨɤ ɡɭɛɨɪɟɡ-
ɧɨɣ 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 ɤɨɥɟ-
ɫɚ.
Ɉɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ Y0 Ɋɏ0 ɨɪɞɢɧɚɬɚ ɬɨɱɤɢ G0 - Y0Go, ɤɨ-
ɬɨɪɭɸ ɞɥɹ ɤɪɚɬɤɨɫɬɢ ɨɛɨɡɧɚɱɢɦ Y0, ɪɚɜɧɚ: |
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Y0 = [ rz (1 - sin α w0 )] - hn0. |
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(2.36) |
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ɒɚɝ ɡɭɛɶɟɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨ ɧɨɪɦɚɥɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ |
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Ɋw0 = 2 πrw1 / z1. |
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Ɍɨɥɳɢɧɚ ɡɭɛɚ ɮɪɟɡɵ ɩɨ ɧɨɪɦɚɥɢ ɧɚ ɧɚɱɚɥɶɧɨɣ ɩɪɹɦɨɣ |
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S |
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n0 |
= P |
− 2r |
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n |
+ invα − invα |
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(2.38) |
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W 0 |
w |
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W 0 . |
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ɉɨɞɪɟɡ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ ɨɬɫɭɬɫɬɜɭɟɬ, ɟɫɥɢ ɜɵɞɟɪɠɢɜɚɟɬɫɹ ɭɫɥɨɜɢɟ:
Υ0 |
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r w ≥ sin2 α w0 . |
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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 ɝɪɚ-
ɧɢɰɭɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ
3
rp = (0,5d cosα )2 + ρ p |
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(2.40) |
ɝɞɟ ρp - ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɜ ɬɨɱɤɟ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟ-
ɦɨɝɨ ɤɨɥɟɫɚ, ɩɨɞɫɱɢɬɵɜɚɟɦɨɝɨ ɩɨ ɮɨɪɦɭɥɟ . 8.
ɍɝɨɥ ɩɪɨɮɢɥɹ ɜ ɬɨɱɤɟ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɧɚɪɟɡɚɟɦɨɝɨ ɤɨɥɟɫɚ
α p |
= arccos |
0,5d cosα |
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(2.4 ) |
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rp |
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ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɬɨɱɤɢ ɨɬ ɨɫɢ Y [9], ɫ.2 4-2 5, (ɪɢɫ.2.2) |
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σ p |
= α w0 − α p . |
(2.42) |
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Ɉɪɞɢɧɚɬɚ ɬɨɱɤɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɮɪɟɡɵ, cɨɨɬɜɟɬɫɬɜɭɸɳɟɣ (ɫɨɩɪɹɝɚɟɦɨɣ)
ɬɨɱɤɟ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ, ɬ.ɟ. ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɬɨɱɤɢ, ɨɬ-
ɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ Y0 Ɋɏ0 |
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Y0P = rp cos σp – rw1 . |
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(2.43) |
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Ɍɨɥɳɢɧɚ ɡɭɛɚ ɮɪɟɡɵ S2 (ɫɦ.ɪɢɫ.2.2), ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɨɛɪɚɛɨɬɤɟ ɚɤɬɢɜ- |
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ɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ |
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Sz= Sn0 |
- 2 Yop tg αw0 . |
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(2.44) |
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Ɇɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɵɣ ɞɥɹ ɩɪɢɧɹɬɨɝɨ ɡɧɚɱɟɧɢɹ ɭɝɥɚ ɩɪɨɮɢɥɹ ɪɚɞɢɭɫ |
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ɡɚɤɪɭɝɥɟɧɢɹ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ (ɪɢɫ.2.2) |
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rɫɨɩɪ = |
(0,5Sh0 − hh0 tgα w0 ) |
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(2.45) |
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α w0 ) |
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cosα w0 ( − sin |
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Ɍɨɥɳɢɧɚ ɡɭɛɚ Sɫɨɩɪ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ rɫɨɩɪ, |
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Sɫɨɩɪ = 2 rɫɨɩɪ cos αw0. |
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(2.46) |
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Ɉɬɫɭɬɫɬɜɢɟ ɡɚɨɫɬɪɟɧɢɹ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɫɥɨɜɢɟɦ: |
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Sɫɨɩɪ ≥ Sz. |
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(2.47) |
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ȿɫɥɢ ɭɫɥɨɜɢɟ 2.47 ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ |
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rz = |
(hh0 + yop ) |
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(2.48) |
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− sinα w0 |
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ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ |
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rz = rɫɨɩɪ |
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Sɫɨɩɪ |
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(2.49) |
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2cosα w0 |
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ɉɪɢ ɞɨɩɭɫɬɢɦɨɫɬɢ ɩɨɞɪɟɡɚ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ ɫɥɟɞɭɟɬ ɩɪɨɜɟɪɢɬɶ, ɧɟ ɧɚ-
ɯɨɞɢɬɫɹ ɥɢ ɨɧ (ɩɨɞɪɟɡ) ɧɚ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ, ɱɬɨ ɧɟɞɨɩɭɫ-
ɬɢɦɨ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɫɥɟɞɭɟɬ ɧɚɣɬɢ ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟɫɚ, ɫ
ɤɨɬɨɪɨɣ ɧɚɱɢɧɚɟɬɫɹ ɩɨɞɪɟɡ, rp′ ɢ ɫɪɚɜɧɢɬɶ ɟɝɨ ɫ ɪɚɞɢɭɫɨɦ ɨɤɪɭɠɧɨɫɬɢ ɤɨɥɟ-
ɫɚ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɧɚɱɚɥɭɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɮɢɥɹ ɡɭɛɚ ɤɨɥɟɫɚ.
Ɋɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ rp |
′ ɦɨɠɧɨ ɧɚɣɬɢ, ɪɟɲɢɜ ɫɢɫɬɟɦɭ ɬɪɚɧɫɰɟɧɞɟɧɬɧɵɯ |
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ɭɪɚɜɧɟɧɢɣ ɷɜɨɥɶɜɟɧɬɵ ɡɭɛɚ ɤɨɥɟɫɚ |
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+ invα − |
π |
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m − Sn |
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invdp′ = ϕ p′ |
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0,5d cosα |
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(2.50) |
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rp′ = |
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cosd |
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ɢ ɩɟɪɟɯɨɞɧɨɣ ɤɪɢɜɨɣ ɫɨɝɥɚɫɧɨ ɜɵɪɚɠɟɧɢɸ 9.5 [9, ɫ.2 6]. |
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σ = arccos |
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y |
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rp′ |
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σ − (0,5S |
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tgα |
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w0 |
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ψ = |
p′ |
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rw |
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(2.5 ) |
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ϕ p′ = σ |
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Ⱥ = invα − |
π m − Sn |
− invα p′ , ɢ ɡɚɞɚɜɲɢɫɶ α p′ ɜ ɩɪɟɞɟ- |
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Ɉɛɨɡɧɚɱɢɜ |
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d |
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ɥɚɯ 0-20° (ɜ ɪɚɞɢɚɧɚɯ 0-0,34906), ɧɚ ɨɫɧɨɜɟ ɚɥɝɨɪɢɬɦɚ ɧɚ ɪɢɫ.2.3 ɢ ɩɪɨɝɪɚɦɦɵ ɞɥɹ ɗȼɆ, ɦɟɬɨɞɨɦ ɢɬɟɪɚɰɢɢ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ α p′ ɢ rp′ .
ȿɫɥɢ rp > rp′ , |
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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 |
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rz ≥ 0,15m. |
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