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Расчет нагрузок на органы управления несущим винтом вертолета одновинтовой схемы..pdf

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Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
ɍȾɄ: 629.735.33.014.16:533.662.6
ɊȺɋɑȿɌ ɇȺȽɊɍɁɈɄ ɇȺ ɈɊȽȺɇɕ ɍɉɊȺȼɅȿɇɂə
ɇȿɋɍɓɂɆ ȼɂɇɌɈɆ ȼȿɊɌɈɅȿɌȺ ɈȾɇɈȼɂɇɌɈȼɈɃ ɋɏȿɆɕ
Ȼ.Ʌ. ȺɊɌȺɆɈɇɈȼ, Ɇ.Ɇ. ɄɊɍɑɂɇɂɇ
ȼ ɫɬɚɬɶɟ ɢɡɥɨɠɟɧ ɦɟɬɨɞ ɪɚɫɱɟɬɚ ɦɨɦɟɧɬɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɨɫɟɜɨɝɨ ɲɚɪɧɢɪɚ ɜɬɭɥɤɢ ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ ɨɬ
ɞɟɣɫɬɜɢɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɢ ɢɧɟɪɰɢɨɧɧɵɯ ɫɢɥ, ɜɨɡɧɢɤɚɸɳɢɯ ɧɚ ɥɨɩɚɫɬɢ. ɉɪɢɧɹɬɵ ɞɨɩɭɳɟɧɢɹ ɨ ɬɨɦ, ɱɬɨ ɥɨɩɚɫɬɢ
ɚɛɫɨɥɸɬɧɨ ɠɟɫɬɤɢɟ ɢ ɢɦɟɸɬ ɩɪɹɦɨɭɝɨɥɶɧɭɸ ɮɨɪɦɭ ɜ ɩɥɚɧɟ. Ɇɚɯɨɜɨɟ ɞɜɢɠɟɧɢɟ ɥɨɩɚɫɬɢ ɨɩɢɫɵɜɚɟɬɫɹ ɫ ɬɨɱɧɨɫɬɶɸ
ɞɨ ɩɟɪɜɨɣ ɝɚɪɦɨɧɢɤɢ ɪɹɞɚ Ɏɭɪɶɟ, ɢɧɞɭɤɬɢɜɧɚɹ ɫɤɨɪɨɫɬɶ ɫɱɢɬɚɟɬɫɹ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɩɨ ɞɢɫɤɭ ɜɢɧɬɚ.
Ⱥɷɪɨɞɢɧɚɦɢɱɟɫɤɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɲɚɪɧɢɪɧɨɝɨ ɦɨɦɟɧɬɚ ɧɚɯɨɞɢɬɫɹ ɱɢɫɥɟɧɧɵɦ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟɦ ɩɨɝɨɧɧɵɯ
ɫɢɥ ɩɨ ɪɚɞɢɭɫɭ ɥɨɩɚɫɬɢ ɫ ɭɱɟɬɨɦ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɨɮɢɥɟɣ, ɩɨɥɭɱɟɧɧɵɯ ɩɨ ɞɚɧɧɵɦ ɢɫɩɵɬɚɧɢɣ ɜ
ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɬɪɭɛɟ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɭɝɥɚɯ ɚɬɚɤɢ ɢ ɱɢɫɥɚɯ Ɇɚɯɚ. Ɇɨɦɟɧɬ ɨɬ ɭɩɪɭɝɢɯ ɫɢɥ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɥɹ
ɜɬɭɥɤɢ ɜɢɧɬɚ ɫ ɩɥɚɫɬɢɧɱɚɬɵɦ ɬɨɪɫɢɨɧɨɦ. ɇɚ ɨɫɧɨɜɟ ɞɚɧɧɵɯ ɨ ɜɟɥɢɱɢɧɚɯ ɲɚɪɧɢɪɧɵɯ ɦɨɦɟɧɬɨɜ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ
ɧɚɝɪɭɡɤɢ ɧɚ ɤɨɥɶɰɟ ɚɜɬɨɦɚɬɚ ɩɟɪɟɤɨɫɚ, ɜɨɡɧɢɤɚɸɳɢɟ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɚɡɢɦɭɬɚɥɶɧɵɯ ɩɨɥɨɠɟɧɢɹɯ ɜɪɚɳɚɸɳɢɯɫɹ ɥɨɩɚɫɬɟɣ ɜɢɧɬɚ.
Ɋɚɫɱɟɬɵ, ɜɵɩɨɥɧɟɧɧɵɟ ɧɚ ɩɪɢɦɟɪɟ ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ ɜɟɪɬɨɥɟɬɚ Ɇɢ-34, ɩɨɤɚɡɚɥɢ, ɱɬɨ ɫɪɟɞɧɢɟ ɡɚ ɨɛɨɪɨɬ
ɧɚɝɪɭɡɤɢ ɜ ɤɚɧɚɥɟ ɭɩɪɚɜɥɟɧɢɹ ɨɛɳɢɦ ɲɚɝɨɦ Ɋɨɲ ɜɨɡɪɚɫɬɚɸɬ ɩɨ ɫɤɨɪɨɫɬɢ ɩɨɥɟɬɚ. ɉɪɢ ɷɬɨɦ ɭɫɢɥɢɹ ɜ ɤɚɧɚɥɟ ɩɪɨɞɨɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ Ɋɩɪɨɞ ɫɨɫɬɚɜɥɹɸɬ ɞɨ 80 % ɨɬ ɭɫɢɥɢɹ ɜ ɤɚɧɚɥɟ ɨɛɳɟɝɨ ɲɚɝɚ, ɚ ɜ ɤɚɧɚɥɟ ɩɨɩɟɪɟɱɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ
Ɋɩɨɩ – ɞɨ 40 %, ɱɬɨ ɯɨɪɨɲɨ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɩɪɢɜɟɞɟɧɧɵɦɢ ɞɚɧɧɵɦɢ ɥɟɬɧɵɯ ɢɫɩɵɬɚɧɢɣ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɧɟɫɭɳɢɣ ɜɢɧɬ, ɲɚɪɧɢɪɧɵɟ ɦɨɦɟɧɬɵ.
Ɋɭɥɟɜɵɟ ɩɪɢɜɨɞɵ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ (ɋɍ) ɧɟɫɭɳɢɦ ɜɢɧɬɨɦ (ɇȼ) ɜɟɪɬɨɥɟɬɚ ɧɚɝɪɭɠɚɸɬɫɹ ɰɢɤɥɢɱɟɫɤɢɦɢ ɧɚɝɪɭɡɤɚɦɢ, ɩɪɢɯɨɞɹɳɢɦɢ ɫ ɥɨɩɚɫɬɟɣ ɨɬ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ, ɭɩɪɭɝɢɯ ɢ
ɢɧɟɪɰɢɨɧɧɵɯ ɫɢɥ. Ⱦɥɹ ɷɮɮɟɤɬɢɜɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɜɟɪɬɨɥɟɬɨɦ ɪɭɥɟɜɵɟ ɩɪɢɜɨɞɵ ɞɨɥɠɧɵ ɛɵɬɶ
ɪɚɫɫɱɢɬɚɧɵ ɧɚ ɷɬɢ ɧɚɝɪɭɡɤɢ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɩɪɢ ɜɵɛɨɪɟ ɩɚɪɚɦɟɬɪɨɜ ɝɢɞɪɨɭɫɢɥɢɬɟɥɟɣ (Ƚɍ)
ɢ ɞɪɭɝɢɯ ɚɝɪɟɝɚɬɨɜ ɋɍ ɜɟɪɬɨɥɟɬɚ ɢɫɩɨɥɶɡɭɸɬɫɹ, ɜ ɨɫɧɨɜɧɨɦ, ɞɚɧɧɵɟ ɥɟɬɧɵɯ ɢ ɫɬɟɧɞɨɜɵɯ ɢɫɩɵɬɚɧɢɣ, ɩɨɫɤɨɥɶɤɭ ɧɟɬ ɞɨɫɬɚɬɨɱɧɨ ɧɚɞɟɠɧɵɯ ɢ ɭɧɢɜɟɪɫɚɥɶɧɵɯ ɦɟɬɨɞɨɜ ɪɚɫɱɟɬɚ ɧɚɝɪɭɡɨɤ ɧɚ ɷɥɟɦɟɧɬɵ ɋɍ ɜɟɪɬɨɥɟɬɚ, ɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ ɧɚ ɜɫɟɯ ɪɟɠɢɦɚɯ ɩɨɥɟɬɚ.
Ɂɚɞɚɱɚ ɪɚɫɱɟɬɚ ɲɚɪɧɢɪɧɵɯ ɦɨɦɟɧɬɨɜ, ɧɚɝɪɭɠɚɸɳɢɯ ɋɍ ɧɟɫɭɳɢɦ ɜɢɧɬɨɦ ɜɟɪɬɨɥɟɬɨɜ,
ɪɚɫɫɦɚɬɪɢɜɚɥɚɫɶ ɦɧɨɝɢɦɢ ɨɬɟɱɟɫɬɜɟɧɧɵɦɢ ɭɱɟɧɵɦɢ [1, 2, 3]. Ɍɚɤ, ɧɚɩɪɢɦɟɪ, ɜ ɪɚɛɨɬɟ [1] ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɩɪɨɛɥɟɦɟ ɦɚɯɨɜɨɝɨ ɮɥɚɬɬɟɪɚ ɇȼ ɧɚ ɪɟɠɢɦɚɯ ɨɫɟɜɨɝɨ ɢ ɤɨɫɨɝɨ ɨɛɬɟɤɚɧɢɹ ɇȼ ɩɨɥɭɱɟɧɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɚɛɫɨɥɸɬɧɨ ɠɟɫɬɤɨɣ ɥɨɩɚɫɬɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɟɜɨɝɨ ɲɚɪɧɢɪɚ, ɨɞɧɚɤɨ ɢɫɫɥɟɞɨɜɚɧɢɟ ɧɚɝɪɭɡɨɤ ɜ ɋɍ ɧɟ ɩɪɨɜɨɞɢɥɨɫɶ. ȼ ɪɚɛɨɬɟ [2] ɫ ɩɨɦɨɳɶɸ
ɬɟɨɪɢɢ ɩɨɞɨɛɢɹ ɪɟɲɚɥɚɫɶ ɡɚɞɚɱɚ ɩɟɪɟɫɱɟɬɚ ɲɚɪɧɢɪɧɨɝɨ ɦɨɦɟɧɬɚ, ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɩɨ ɢɫɩɵɬɚɧɢɹɦ ɦɨɞɟɥɢ ɜ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɬɪɭɛɟ, ɧɚ ɢɫɫɥɟɞɭɟɦɵɣ ɜɚɪɢɚɧɬ ɜɟɪɬɨɥɟɬɚ. ɇɨ ɚɥɝɨɪɢɬɦ ɪɚɫɱɟɬɚ
ɲɚɪɧɢɪɧɨɝɨ ɦɨɦɟɧɬɚ ɞɥɹ ɥɨɩɚɫɬɢ ɩɪɨɢɡɜɨɥɶɧɨɣ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɢ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɤɨɦɩɨɧɨɜɤɢ ɧɟ ɩɪɢɜɨɞɢɬɫɹ.
ɇɚɢɛɨɥɟɟ ɩɨɞɪɨɛɧɨ ɩɪɨɛɥɟɦɚ ɪɚɫɱɟɬɚ ɲɚɪɧɢɪɧɨɝɨ ɦɨɦɟɧɬɚ ɧɚ ɜɬɭɥɤɟ ɇȼ ɢ ɭɫɢɥɢɣ,
ɜɨɡɧɢɤɚɸɳɢɯ ɨɬ ɧɟɝɨ ɜ ɋɍ, ɪɚɫɫɦɨɬɪɟɧɚ ɜ ɦɨɧɨɝɪɚɮɢɢ [3]. Ɂɞɟɫɶ ɬɚɤ ɠɟ, ɤɚɤ ɜ ɪɚɛɨɬɟ [1],
ɩɨɥɭɱɟɧɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɚɛɫɨɥɸɬɧɨ ɠɟɫɬɤɨɣ ɥɨɩɚɫɬɢ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɨɫɟɜɨɝɨ ɲɚɪɧɢɪɚ ɫ ɭɱɟɬɨɦ ɫɨɫɬɚɜɥɹɸɳɢɯ ɲɚɪɧɢɪɧɨɝɨ ɦɨɦɟɧɬɚ ɨɬ ɢɡɝɢɛɧɵɯ ɢ ɤɪɭɬɢɥɶɧɵɯ
ɤɨɥɟɛɚɧɢɣ ɥɨɩɚɫɬɢ. ɉɨɤɚɡɚɧ ɩɪɢɦɟɪɧɵɣ ɜɢɞ ɡɚɜɢɫɢɦɨɫɬɢ ɭɫɢɥɢɣ ɜ ɫɢɫɬɟɦɟ ɩɪɨɞɨɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɢ ɭɩɪɚɜɥɟɧɢɹ ɨɛɳɢɦ ɲɚɝɨɦ, ɧɨ ɚɥɝɨɪɢɬɦɚ ɪɚɫɱɟɬɚ ɭɫɢɥɢɣ ɞɥɹ ɡɚɞɚɧɧɨɣ ɥɨɩɚɫɬɢ ɧɟ ɩɪɢɜɨɞɢɬɫɹ.
ȼ ɞɨɤɥɚɞɟ [6] ɪɚɫɫɦɨɬɪɟɧ ɦɟɬɨɞ ɪɚɫɱɟɬɚ ɲɚɪɧɢɪɧɵɯ ɦɨɦɟɧɬɨɜ ɫ ɭɱɟɬɨɦ ɭɩɪɭɝɨɫɬɢ ɥɨɩɚɫɬɟɣ ɜ ɩɥɨɫɤɨɫɬɹɯ ɬɹɝɢ, ɜɪɚɳɟɧɢɹ ɢ ɤɪɭɱɟɧɢɹ. Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɯɨɪɨɲɨ ɫɨɜɩɚɞɚɸɬ ɫ ɥɟɬɧɵɦ
ɷɤɫɩɟɪɢɦɟɧɬɨɦ ɞɥɹ ɪɟɠɢɦɨɜ ɩɨɥɟɬɚ ɫɨ ɫɪɟɞɧɢɦɢ ɫɤɨɪɨɫɬɹɦɢ, ɧɨ ɢɦɟɸɬɫɹ ɡɧɚɱɢɬɟɥɶɧɵɟ ɪɚɫɯɨɠɞɟɧɢɟ ɧɚ ɦɚɥɵɯ ɢ ɦɚɤɫɢɦɚɥɶɧɵɯ ɫɤɨɪɨɫɬɹɯ ɩɨɥɟɬɚ ɜɟɪɬɨɥɟɬɚ.
ɉɨɷɬɨɦɭ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɰɟɥɟɫɨɨɛɪɚɡɧɵɦ ɪɟɲɢɬɶ ɡɚɞɚɱɭ ɨɛ ɨɩɪɟɞɟɥɟɧɢɢ ɧɚɝɪɭɡɨɤ, ɩɪɢɯɨɞɹɳɢɯ ɧɚ ɨɪɝɚɧɵ ɭɩɪɚɜɥɟɧɢɹ ɧɟɫɭɳɢɦ ɜɢɧɬɨɦ, ɧɚ ɩɪɢɦɟɪɟ ɜɟɪɬɨɥɟɬɚ ɫ ɢɡɜɟɫɬɧɵɦɢ ɩɚɪɚɦɟɬ139
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɪɚɦɢ ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ, ɜɬɭɥɤɢ, ɚɜɬɨɦɚɬɚ ɩɟɪɟɤɨɫɚ (Ⱥɉ), ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɩɪɨɮɢɥɟɣ ɢ ɫɪɚɜɧɢɬɶ ɢɯ ɫ ɞɚɧɧɵɦɢ ɥɟɬɧɵɯ ɢɫɩɵɬɚɧɢɣ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɨɜ ɩɨɥɟɬɚ
ɜɟɪɬɨɥɟɬɚ.
ɈȻɓȺə ɉɈɋɌȺɇɈȼɄȺ ɁȺȾȺɑɂ
Ɋɚɫɫɦɨɬɪɢɦ ɇȼ ɫ ɱɢɫɥɨɦ ɥɨɩɚɫɬɟɣ, ɪɚɜɧɵɦ kɥ (ɪɢɫ. 1). ɍɫɢɥɢɹ ɜ ɫɢɫɬɟɦɟ ɭɩɪɚɜɥɟɧɢɹ ɇȼ ɪɚɫɩɪɟɞɟɥɹɸɬɫɹ ɢ ɜɨɫɩɪɢɧɢɦɚɸɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ȼɟɪɬɢɤɚɥɶɧɵɟ ɬɹɝɢ, ɫɨɟɞɢɧɹɸɳɢɟ ɪɵɱɚɝ ɩɨɜɨɪɨɬɚ ɥɨɩɚɫɬɢ ɫ ɬɚɪɟɥɤɨɣ Ⱥɉ, ɧɚɝɪɭɠɚɸɬɫɹ ɨɫɟɜɵɦɢ ɫɢɥɚɦɢ ɨɬ ɤɚɠɞɨɣ ɥɨɩɚɫɬɢ. ɉɪɢ ɷɬɨɦ ɞɟɬɚɥɢ ɋɍ, ɫɨɟɞɢɧɹɸɳɢɟ Ⱥɉ ɫ Ƚɍ, ɚ ɬɚɤɠɟ ɞɟɬɚɥɢ ɤɪɟɩɥɟɧɢɹ Ƚɍ ɧɚɝɪɭɠɚɸɬɫɹ ɫɭɦɦɚɪɧɨɣ ɨɫɟɜɨɣ ɫɢɥɨɣ P™ ɢ ɦɨɦɟɧɬɚɦɢ ɨɬ ɜɫɟɯ ɥɨɩɚɫɬɟɣ ɇȼ. ɉɪɢ ɷɬɨɦ P™ ɧɚɝɪɭɠɚɟɬ ɲɬɨɤ
Ƚɍ ɨɛɳɟɝɨ ɲɚɝɚ, ɚ Mx ɢ Mz ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ – ɲɬɨɤɢ Ƚɍ ɩɨɩɟɪɟɱɧɨɝɨ ɢ ɩɪɨɞɨɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ.
ȼ ɤɚɱɟɫɬɜɟ ɞɨɩɭɳɟɧɢɣ ɩɪɢɦɟɦ:
– ɥɨɩɚɫɬɢ ɇȼ ɚɛɫɨɥɸɬɧɨ ɠɟɫɬɤɢɟ (ɭɩɪɭɝɢɯ ɞɟɮɨɪɦɚɰɢɣ – ɧɟɬ),
– Ȧ (ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɇȼ) ɧɟ ɡɚɜɢɫɢɬ ɨɬ
ɜɪɟɦɟɧɢ,
– ɬɹɝɢ ɩɨɜɨɪɨɬɚ ɥɨɩɚɫɬɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵ ɩɥɨɫɤɨɫɬɢ ɜɪɚɳɟɧɢɹ ɇȼ,
– ɥɨɩɚɫɬɢ ɇȼ ɢɦɟɸɬ ɩɪɹɦɨɭɝɨɥɶɧɭɸ ɮɨɪɦɭ
ɜ ɩɥɚɧɟ,
– ɨɫɶ ɨɫɟɜɨɝɨ ɲɚɪɧɢɪɚ ɥɟɠɢɬ ɧɚ ɯɨɪɞɟ ɥɨɩɚɫɬɢ.
Ⱦɥɹ k-ɥɨɩɚɫɬɧɨɝɨ ɜɢɧɬɚ ɫɩɪɚɜɟɞɥɢɜɵ ɫɥɟɞɭɸɳɢɟ ɨɬɧɨɊɢɫ. 1. ɇɚɝɪɭɡɤɢ ɧɚ ɬɚɪɟɥɤɭ ɚɜɬɨɦɚɬɚ
ɩɟɪɟɤɨɫɚ, ɩɪɢɯɨɞɹɳɢɟ ɫ ɥɨɩɚɫɬɢ ɇȼ
ɲɟɧɢɹ i = 1…, kɥ:
kɥ
kɥ
kɥ
i =1
i =1
i =1
PΣ (ψ ) = ¦ Pi (ψ i ), M z (ψ ) = RȺɉ ¦ Pi (ψ i ) cosψ i , M x (ψ ) = − RȺɉ ¦ Pi (ψ i ) sinψ i ,
ψ i = ψ + Δψ ɥ (i − 1), Δψ ɥ =
2π
.
kɥ
Ȼɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɜɚɡɢɭɫɬɚɧɨɜɢɜɲɢɟɫɹ ɪɟɠɢɦɵ ɩɨɥɟɬɚ, ɧɚ ɤɨɬɨɪɵɯ ɫɢɥɵ ɢ ɦɨɦɟɧɬɵ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɜɟɪɬɨɥɟɬ, ɫɛɚɥɚɧɫɢɪɨɜɚɧɵ. Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ
ɦɨɦɟɧɬɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɟɜɨɝɨ ɲɚɪɧɢɪɚ i-ɣ ɥɨɩɚɫɬɢ
(ɪɢɫ. 2):
M Pi − M ɢɧɟɪ − M ɬɨɪ + M ɚɷɪɨ = 0.
Ɋɢɫ. 2. ɋɢɥɵ ɢ ɦɨɦɟɧɬɵ, ɞɟɣɫɬɜɭɸɳɢɟ
ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɟɜɨɝɨ ɲɚɪɧɢɪɚ
Ɂɞɟɫɶ
M Pi = Px
i ɩ cos ϕ – ɦɨɦɟɧɬ ɨɬ ɫɢɥɵ ɫ ɩɨɜɨɞɤɚ i-ɣ ɥɨɩɚɫɬɢ,
Ɇɢɧɟɪ – ɦɨɦɟɧɬ ɢɧɟɪɰɢɨɧɧɵɯ ɫɢɥ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ Ɉɒ i-ɣ ɥɨɩɚɫɬɢ;
Ɇɬɨɪ – ɦɨɦɟɧɬ ɫɢɥ ɭɩɪɭɝɨɫɬɢ ɜ ɨɫɟɜɨɦ ɲɚɪɧɢɪɟ i-ɣ ɥɨɩɚɫɬɢ;
Ɇɚɷɪɨ – ɦɨɦɟɧɬ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ i-ɸ ɥɨɩɚɫɬɶ.
ɂɡ ɭɪɚɜɧɟɧɢɹ ɦɨɦɟɧɬɨɜ ɫɥɟɞɭɟɬ:
Pi =
−(− M ɢɧɟɪ − M ɬɨɪɫ + M ɚɷɪɨ )
xɩ cos ϕ
140
=
−M Σ
.
xɩ cos ϕ
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɡɚɞɚɱɚ ɫɜɨɞɢɬɫɹ ɤ ɧɚɯɨɠɞɟɧɢɸ ɫɭɦɦɚɪɧɨɝɨ ɦɨɦɟɧɬɚ M™, ɞɟɣɫɬɜɭɸɳɟɝɨ
ɧɚ ɥɨɩɚɫɬɶ ɨɬɧɨɫɢɬɟɥɶɧɨ Ɉɒ.
R
x
Ɂɚɞɚɱɭ ɛɭɞɟɦ ɪɟɲɚɬɶ ɜ ɛɟɡɪɚɡɦɟɪɧɨɦ ɜɢɞɟ, ɨɩɪɟɞɟɥɢɜ: RȺɉ = Ⱥɉ , xɉ = ɉ .
R
R
Ɍɨɝɞɚ ɤɨɷɮɮɢɰɢɟɧɬɵ ɨɫɟɜɵɯ ɫɢɥ i-ɯ ɥɨɩɚɫɬɟɣ ɛɭɞɭɬ ɪɚɜɧɵ
CPi =
− mΣ
.
xɉ cos ϕ
Ʉɨɷɮɮɢɰɢɟɧɬ ɫɭɦɦɚɪɧɨɣ ɨɫɟɜɨɣ ɫɢɥɵ, ɩɪɨɞɨɥɶɧɨɝɨ ɢ ɩɨɩɟɪɟɱɧɨɝɨ ɦɨɦɟɧɬɨɜ ɭɩɪɚɜɥɟɧɢɹ:
kɥ
kɥ
kɥ
i =1
i =1
i =1
ɋ P (ψ ) = ¦ C Pi (ψ i ), mz (ψ ) = RȺɉ ¦ CPi (ψ i ) cosψ i , mx (ψ ) = − RȺɉ ¦ C Pi (ψ i ) sinψ i ,
PΣ = CP
ρ
2
(ω R ) 2 π R 2 , M z = mz
ρ
2
(ω R ) 2 π R 3 , M x = mx
ρ
2
(ω R ) 2 π R 3 .
ɆɈɆȿɇɌ ɈɌ ȺɗɊɈȾɂɇȺɆɂɑȿɋɄɂɏ ɋɂɅ
Ɉɫɧɨɜɭ ɪɚɫɱɟɬɚ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɇȼ ɫɨɫɬɚɜɥɹɟɬ ɦɟɬɨɞ ɨɩɪɟɞɟɥɟɧɢɹ ɢɧɞɭɤɬɢɜɧɵɯ ɫɤɨɪɨɫɬɟɣ. ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɩɪɢɦɟɧɹɟɬɫɹ ɨɛɨɛɳɟɧɧɚɹ ɞɢɫɤɨɜɚɹ ɜɢɯɪɟɜɚɹ ɬɟɨɪɢɹ ɇȼ
[4], ɩɨɡɜɨɥɹɸɳɚɹ ɪɚɫɫɱɢɬɚɬɶ ɩɨɥɟ ɢɧɞɭɤɬɢɜɧɵɯ ɫɤɨɪɨɫɬɟɣ ɜ ɲɢɪɨɤɨɦ ɞɢɚɩɚɡɨɧɟ ɭɝɥɨɜ ɚɬɚɤɢ ɢ
ɫɤɨɪɨɫɬɟɣ ɧɚɛɟɝɚɸɳɟɝɨ ɩɨɬɨɤɚ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɝɥɚ ɧɚɤɥɨɧɚ ɜɢɯɪɟɜɨɣ ɫɢɫɬɟɦɵ ɇȼ, ɩɪɟɞɫɬɚɜɥɹɸɳɟɣ ɫɨɛɨɣ ɫɤɨɲɟɧɧɵɣ ɩɨɥɭɛɟɫɤɨɧɟɱɧɵɣ ɜɢɯɪɟɜɨɣ ɰɢɥɢɧɞɪ, ɩɪɢɦɟɧɹɟɬɫɹ ɦɨɞɟɥɶ ɇȼ ɫ
ɪɚɜɧɨɦɟɪɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɜɨɡɞɭɲɧɨɣ ɧɚɝɪɭɡɤɢ ɩɨ ɞɢɫɤɭ. ɍɝɨɥ ɧɚɤɥɨɧɚ ɨɫɢ ɜɢɯɪɟɜɨɣ ɤɨɥɨɧɧɵ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɢ ɭɝɥɚ ɚɬɚɤɢ ɧɚɛɟɝɚɸɳɟɝɨ ɧɚ ɇȼ ɩɨɬɨɤɚ [7].
Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɦɨɦɟɧɬɚ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɥɨɩɚɫɬɶ ɇȼ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɟɜɨɝɨ ɲɚɪɧɢɪɚ, ɪɚɫɫɦɨɬɪɢɦ ɩɪɨɮɢɥɶ ɥɨɩɚɫɬɢ ɧɚ ɩɪɨɢɡɜɨɥɶɧɨɦ ɪɚɞɢɭɫɟ r (ɪɢɫ. 3). Ɍɨɝɞɚ
1
mɚɷɪɨ = ³ dCR (r )( xɨɲ − xɞ ).
r0
ɋɨɫɬɚɜɥɹɸɳɚɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɥɵ ɧɚ ɭɱɚɫɬɤɟ dr ɛɭɞɟɬ ɪɚɜɧɚ
dC R = (C y cos α + C x sin α )W 2bdr ,
ɝɞɟ
W = Wx2 + W y2 ,
Wx = r + μ sinψ ,
Wy = λ + vδ ,
Ɋɢɫ. 3. Ⱥɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɫɢɥɵ ɧɚ ɩɪɨɮɢɥɟ ɥɨɩɚɫɬɢ
141
vδ = − β ɥ μ cosψ −
∂β ɥ
r.
∂ψ
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɍɝɨɥ ɜɡɦɚɯɚ ɥɨɩɚɫɬɢ ȕɥ ɨɩɢɫɵɜɚɟɬɫɹ ɩɟɪɜɨɣ ɝɚɪɦɨɧɢɤɨɣ ɪɹɞɚ Ɏɭɪɶɟ:
ȕɥ = ɚ0 – ɚ1cosȥ – b1sinȥ,
a + kb
b − ka10
+ D1η + D2κ .
a1 = 10 2 10 + D1κ − D2η , b1 = 10
1+ k
1+ k 2
Ɂɞɟɫɶ ț ɢ Ș – ɭɝɥɵ ɨɬɤɥɨɧɟɧɢɹ ɚɜɬɨɦɚɬɚ ɩɟɪɟɤɨɫɚ ɜ ɩɪɨɞɨɥɶɧɨɦ ɢ ɩɨɩɟɪɟɱɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ.
Ʉɨɷɮɮɢɰɢɟɧɬɵ D1 ɢ D2 ɡɚɜɢɫɹɬ ɨɬ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ ɜɬɭɥɤɢ ɇȼ (ɪɢɫ. 4):
RȺɉ
cos(σ − C0 − Δψ ɭɩɪ ) ,
xɩ
D2 =
RȺɉ
sin(σ − C0 − Δψ ɭɩɪ ) ,
xɩ
σ – ɭɝɨɥ ɤɨɦɩɟɧɫɚɬɨɪɚ ɜɡɦɚɯɚ;
ɝɞɟ
Ɋɢɫ. 4. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɜɬɭɥɤɢ ɇȼ
D1 =
C0 – ɭɝɨɥ, ɜɵɡɜɚɧɧɵɣ ɪɚɡɧɨɫɨɦ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ ɲɚɪɧɢɪɨɜ;
ǻȥɭɩɪ – ɭɝɨɥ ɨɩɟɪɟɠɟɧɢɹ ɭɩɪɚɜɥɟɧɢɹ.
Ⱦɥɹ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɥɨɩɚɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɵ
ɦɚɯɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɩɪɢ ɧɟɣɬɪɚɥɶɧɨɦ ɩɨɥɨɠɟɧɢɢ
ɤɨɥɶɰɚ Ⱥɉ ɧɚɯɨɞɹɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ
4§
4
§4
·
·
2 μv ¨ ϕ0 ɷ + λ ¸
μv a0 + kδ v yɫɪ ¸
¨
1 º
π
ª1
©3
¹, b = 3©
¹,
a0 = γ ɥ « (1 + μv 2 )ϕ0 ɷ + λ » , a10 =
10
1
1
4
3
2
2
¬
¼
1 − μv
1 + μv
2
2
ɝɞɟ Ȗɥ – ɢɧɟɪɰɢɨɧɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɥɨɩɚɫɬɢ:
γɥ =
a∞ ρ b7 R 4
,
2 J ɝɲ
ϕ0ɷ – ɭɝɨɥ ɭɫɬɚɧɨɜɤɢ ɯɚɪɚɤɬɟɪɧɨɝɨ ɫɟɱɟɧɢɹ ɥɨɩɚɫɬɢ ɧɚ r = 0, 7 ɫ ɭɱɟɬɨɦ ɞɟɣɫɬɜɢɹ ɪɟɝɭɥɹɬɨɪɚ
ɜɡɦɚɯɚ:
ϕ0 ɷ = ϕ0 − ka0 ,
ɝɞɟ k = tgσ – ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɦɩɟɧɫɚɬɨɪɚ ɜɡɦɚɯɚ, ij0 – ɭɝɨɥ ɨɛɳɟɝɨ ɲɚɝɚ;
μ v = V cos α ɜ + vxɫɪ , λ = V sin α ɜ − v yɫɪ .
Ɉɩɪɟɞɟɥɢɦ ɭɝɨɥ ɚɬɚɤɢ ɜ ɫɟɱɟɧɢɢ ɥɨɩɚɫɬɢ ɧɚ ɪɚɞɢɭɫɟ r :
α (r ,ψ ) = ϕ (r ,ψ ) + β (r ,ψ ) .
142
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɭɩɪɚɜɥɟɧɢɹ ɭɝɨɥ ɭɫɬɚɧɨɜɤɢ ɥɨɩɚɫɬɟɣ ɰɢɤɥɢɱɟɫɤɢ ɢɡɦɟɧɹɟɬɫɹ ɩɨ ɩɟɪɜɨɣ
ɝɚɪɦɨɧɢɤɟ:
ϕ (r ,ψ ) = ϕ0 ɷ + Δϕ (r ) − ϕc cosψ − ϕs sinψ ,
ɝɞɟ
ϕc = D1η + D2κ − ka1 , ϕ s = − D1κ + D2η − kb1 ,
a1 =
a10 + kb10
b + ka10
, b1 = 10
,
2
1+ k
1+ k 2
ȕ – ɭɝɨɥ ɩɪɢɬɟɤɚɧɢɹ ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ ɜ ɫɟɱɟɧɢɢ ɥɨɩɚɫɬɢ:
§ Wy ·
¸¸ .
© Wx ¹
β = arctg ¨¨
ɋɪɟɞɧɹɹ ɢɧɞɭɤɬɢɜɧɚɹ ɫɤɨɪɨɫɬɶ, ɧɨɪɦɚɥɶɧɚɹ ɤ ɩɥɨɫɤɨɫɬɢ ɞɢɫɤɚ ɇȼ, ɪɚɜɧɚ
v yɫɪ =
1ª
−V cos(α ɤɥ + δ ) + V 2 cos 2 (α ɤɥ + δ ) + ɫɬ º ,
¬
¼
2
ɝɞɟ į – ɭɝɨɥ ɧɚɤɥɨɧɚ ɨɫɢ ɜɢɯɪɟɜɨɝɨ ɰɢɥɢɧɞɪɚ [7].
ɍɝɨɥ ɚɬɚɤɢ α ɤɥ ɨɬɫɱɢɬɵɜɚɟɬɫɹ ɨɬ ɩɥɨɫɤɨɫɬɢ ɤɨɧɰɨɜ ɚɛɫɨɥɸɬɧɨ ɠɟɫɬɤɢɯ ɥɨɩɚɫɬɟɣ ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ:
Į ɤɥ =Į ɜ + ɚ1 .
ɋɪɟɞɧɹɹ ɢɧɞɭɤɬɢɜɧɚɹ ɫɤɨɪɨɫɬɶ ɜ ɩɥɨɫɤɨɫɬɢ ɞɢɫɤɚ ɇȼ
§π δ ·
vxɫɪ = kδ v yɫɪ , kδ = tg ¨ − ¸ .
©4 2 ¹
Ʉɨɷɮɮɢɰɢɟɧɬ ɫɢɥɵ ɬɹɝɢ ɧɚɯɨɞɢɦ ɦɟɬɨɞɨɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ ɩɪɢɛɥɢɠɟɧɢɣ:
ɫɬ =
σ7
2π
2π
1
0
r0
³ dψ ³ ( C ypWx + CxpWy )Wdr .
Ⱦɥɹ ɧɚɣɞɟɧɧɵɯ ɫɤɨɪɨɫɬɟɣ Wx , Wy ɢ ɭɝɥɨɜ ɚɬɚɤɢ Į ɜ ɫɟɱɟɧɢɢ ɥɨɩɚɫɬɢ ɧɚɯɨɞɢɦ ɡɧɚɱɟɧɢɹ
Cyp, Cxp, mzp, ɢɫɩɨɥɶɡɭɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɨɮɢɥɟɣ ɩɨ ɞɚɧɧɵɦ ɷɤɫɩɟɪɢɦɟɧɬɚ
Cyp(Į, M), Cxp(Į, M), mzp(Į, M).
ɉɪɨɢɧɬɟɝɪɢɪɨɜɚɜ ɩɨ ɪɚɞɢɭɫɭ ɥɨɩɚɫɬɢ, ɧɚɣɞɟɦ ɤɨɷɮɮɢɰɢɟɧɬ ɦɨɦɟɧɬɚ ɨɬ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɥɨɩɚɫɬɶ:
1
mɚɷɪɨ = ³ ( C yp cos α + Cxp sin α )W 2b ( xɨɲ − xɞ )dr .
r0
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Ʉɨɨɪɞɢɧɚɬɵ ɰɟɧɬɪɚ ɞɚɜɥɟɧɢɹ ɨɩɪɟɞɟɥɢɦ ɢɡ ɭɪɚɜɧɟɧɢɹ ɦɨɦɟɧɬɨɜ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɩɥɨɫɤɨɫɬɶ ɜɪɚɳɟɧɢɹ ɇȼ:
xɞ = −
mzp b
.
C yp cos α + Cxp sin α
Ɍɨɝɞɚ
1
mɚɷɪɨ = ³ ª¬ xɨɲ ( C yp cos α + Cxp sin α ) + mzp b º¼W 2bdr .
r0
ɆɈɆȿɇɌ ɈɌ ɍɉɊɍȽɂɏ ɋɂɅ
Ɋɚɫɫɦɨɬɪɢɦ ɜ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɜɬɭɥɤɭ ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ ɜɟɪɬɨɥɟɬɚ Ɇɢ-34 ɫ ɭɧɢɜɟɪɫɚɥɶɧɵɦ ɬɨɪɫɢɨɧɨɦ. ɋɯɟɦɚ ɧɚɝɪɭɠɟɧɢɹ ɬɨɪɫɢɨɧɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 5. Ɉɩɪɟɞɟɥɢɦ ɦɨɦɟɧɬ, ɤɨɬɨɪɵɣ ɧɚɞɨ ɩɪɢɥɨɠɢɬɶ ɤ ɬɨɪɫɢɨɧɭ, ɱɬɨɛɵ ɡɚɤɪɭɬɢɬɶ ɟɝɨ ɧɚ ɭɝɨɥ ϕ .
ɗɬɨɬ ɦɨɦɟɧɬ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ [5]
Ɇɬɨɪɫ = Ɇɭɩɪ + Ɇɰɛ,
ɝɞɟ Ɇɭɩɪ – ɦɨɦɟɧɬ, ɫɨɡɞɚɜɚɟɦɵɣ ɫɢɥɚɦɢ ɭɩɪɭɝɨɫɬɢ ɩɥɚɫɬɢɧ; Ɇɰɛ – ɦɨɦɟɧɬ, ɫɨɡɞɚɜɚɟɦɵɣ ɰɟɧɬɪɨɛɟɠɧɨɣ ɫɢɥɨɣ ɩɪɢ ɫɦɟɳɟɧɢɢ ɩɥɚɫɬɢɧ ɬɨɪɫɢɨɧɚ. ɐɟɧɬɪɨɛɟɠɧɚɹ ɫɢɥɚ Nɰɛ ɩɨɜɟɪɧɭɬɚ ɤ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɩɨɞ ɭɝɥɨɦ C0.
ɉɪɢ ɡɚɤɪɭɬɤɟ ɬɨɪɫɢɨɧɚ ɧɚ ɭɝɨɥ ϕ , ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɜɟɬɜɟɣ (1) (2) ɛɭɞɟɬ ɪɚɜɟɧ
§γ
·
§γ
·
ϕ ɡ1 = ϕ cos ¨ + C0 ¸ , ϕ ɡ 2 = ϕ cos ¨ − C0 ¸ .
©2
¹
©2
¹
Ʉɪɭɬɹɳɢɣ ɦɨɦɟɧɬ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧ ɜɵɪɚɠɟɧɢɟɦ:
Mk =
bδ
GJ ɬϕ ɡ
, Jɬ = ɬ
3
Lɬ
3
ɬ
,
ɝɞɟ G – ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ ɜɬɨɪɨɝɨ ɪɨɞɚ ɩɥɚɫɬɢɧ ɬɨɪɫɢɨɧɚ, Jɬ – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɫɟɱɟɧɢɹ ɬɨɪɫɢɨɧɚ ɩɪɢ ɤɪɭɱɟɧɢɢ, Lɬ – ɞɥɢɧɚ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɭɱɚɫɬɤɚ ɩɥɚɫɬɢɧɵ ɬɨɪɫɢɨɧɚ, bɬ – ɲɢɪɢɧɚ ɩɥɚɫɬɢɧɵ, įɬ – ɬɨɥɳɢɧɚ ɩɥɚɫɬɢɧɵ.
Ɋɢɫ. 5. ɇɚɝɪɭɡɤɢ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɬɨɪɫɢɨɧ
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Ⱦɥɹ ɨɛɟɢɯ ɜɟɬɜɟɣ ɢ ɤɨɥɢɱɟɫɬɜɚ ɩɥɚɫɬɢɧ ɜ ɬɨɪɫɢɨɧɟ nT ɩɨɥɭɱɚɟɦ:
γ
M ɭɩɪ = ϕ cos cos C0
2
2Gnɬ bɬδ 3ɬ
.
3Lɬ
N ɰɛ
nδ
ɩɪɢɥɨɠɟɧɚ ɧɚ ɩɥɟɱɟ L = ɬ ɬ ɨɬ ɩɪɨɞɨɥɶɧɨɣ ɨɫɢ ɬɨɪɫɢɨɧɚ, ɢ ɩɨɥɚ2
4
ɝɚɹ ɜ ɛɟɡɪɚɡɦɟɪɧɨɦ ɜɢɞɟ ɩɨɥɭɱɢɦ:
ɋɱɢɬɚɹ, ɱɬɨ ɫɢɥɚ
N ɰɛ = mɥω 2
nδ
R
γ
, M ɰɛ = ϕ cos cos C0 ɬ ɬ mɥω 2 R ,
2
16
2
mɬɨɪɫ = Ʉ1ij,
ɝɞɟ Ʉ1 – ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɩɚɪɚɦɟɬɪɨɜ ɥɨɩɚɫɬɢ ɢ ɬɨɪɫɢɨɧɚ:
Ʉ1 =
§ 2ɋ 2
m
G
γ
1 ·
Ʉ = ɥ3 .
nɬδ ɬ cos cos C0 ¨
δ ɬ bɬ + K ¸ , C =
2 ,
ρ (ω R)
ρR
π
2
8 ¹
© 3Lɬ
2
ɆɈɆȿɇɌ ɈɌ ɂɇȿɊɐɂɈɇɇɕɏ ɋɂɅ
Ɇɨɦɟɧɬ ɢɧɟɪɰɢɨɧɧɵɯ ɫɢɥ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɟɜɨɝɨ ɲɚɪɧɢɪɚ ɜɵɱɢɫɥɹɟɦ ɤɚɤ
M ɢɧɟɪ = J ɨɲ
∂ 2ϕ
,
∂t 2
ɝɞɟ Jɨɲ – ɦɚɫɫɨɜɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɥɨɩɚɫɬɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɟɜɨɝɨ ɲɚɪɧɢɪɚ. Ɍɨɝɞɚ
mɢɧɟɪ =
A
π
(ϕc cosψ + ϕ s sinψ ) ,
A=
2J ɨɲ
.
ρ R5
ɇȺȽɊɍɁɄɂ ɇȺ ɈɊȽȺɇȺɏ ɍɉɊȺȼɅȿɇɂə
Ɋɚɫɫɦɨɬɪɢɦ ɜ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɇȼ ɜɟɪɬɨɥɟɬɚ Ɇɢ-34. Ɉɧ ɢɦɟɟɬ 4 ɥɨɩɚɫɬɢ ɫ ɩɪɨɮɢɥɟɦ
NACA 230 -10M.
ɉɚɪɚɦɟɬɪɵ ɜɬɭɥɤɢ, Ⱥɉ, ɥɨɩɚɫɬɢ ɜɟɪɬɨɥɟɬɚ Ɇɢ-34:
ı7 = 0,0056; r0 = 0,2; ¨ijȈ = 7º; k = 0,54; D1 = 1,4; D2 = 0; Ȗɥ = 3,78; b = 0,044;
RȺɉ = 0,04; xɩ = 0,024; xɨɲ = 0,01; Ȗ = 20,4Û; C0 = 5,2Û; Lɬ = 0,1; bɬ = 0,0006; nɬ = 17;
δ ɬ = 0,000006; mɥ = 13,238 ɤɝ; Rɥ = 5 ɦ; Jɨɲ = 0,056 ɤɝ×ɦ2.
ɇɚ ɪɢɫ. 6, 7, 8 ɩɪɟɞɫɬɚɜɥɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ ɭɫɢɥɢɣ ɜ ɤɚɧɚɥɚɯ ɭɩɪɚɜɥɟɧɢɹ ɜɟɪɬɨɥɟɬɨɦ ɨɬ
ɚɡɢɦɭɬɚɥɶɧɨɝɨ ɩɨɥɨɠɟɧɢɹ ɥɨɩɚɫɬɢ ɧɚ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɚɯ ɩɨɥɟɬɚ.
Pɨɲ = PȈ, Ɋɩɪɨɞ =
M cos γ − M z sin γ
M x sin γ + M z cos γ
, Ɋɩɨɩ = x
,
Rɩɨɩ
Rɩɪɨɞ
ɝɞɟ Rɩɪɨɞ, Rɩɨɩ – ɪɚɞɢɭɫɵ ɤɪɟɩɥɟɧɢɹ ɬɹɝ ɩɪɨɞɨɥɶɧɨɝɨ ɢ ɩɨɩɟɪɟɱɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɤ Ⱥɉ.
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Vol. 19, ʋ 04, 2016
Pɩɪɨɞ, ɤɝɫ
Pɨɲ, ɤɝɫ
Pɩɨɩ, ɤɝɫ
100
100
60
80
80
40
60
60
20
40
40
20
20
ʗ
0
0
ʗ
ʗ
0
90
180
270
360
-20
0
0
90
180
270
360
0
90
180
270
360
-40
ʧʿ V=200̡̥/̸, ʔ=11?
ʿ̨̡̭̌̔̌, ʔ=11?
ʧʿ V=200̡̥/̸, ʔ=11?
ʦ̛̬̙̌ V=150̡̥/̸, ʔ=9?
ʧʿ V=200̡̥/̸, ʔ=11϶
ʦ̛̬̙̌ V=150̡̥/̸, ʔ=9϶
ʦ̛̬̙̌ V=150̡̥/̸, ʔ=9?
ʧʿ V=100̡̥/̸, ʔ=8?
ʿ̨̡̭̌̔̌, ʔ=11?
ʧʿ V=100̡̥/̸, ʔ=8?
ʿ̨̡̭̌̔̌, ʔ=11϶
ʧʿ V=100̡̥/̸, ʔ=8϶
Ɋɢɫ. 6. ɍɫɢɥɢɟ ɜ ɤɚɧɚɥɟ
ɨɛɳɟɝɨ ɲɚɝɚ
Ɋɢɫ. 7. ɍɫɢɥɢɟ ɜ ɤɚɧɚɥɟ
ɩɪɨɞɨɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ
Ɋɢɫ. 8. ɍɫɢɥɢɟ ɜ ɤɚɧɚɥɟ
ɩɨɩɟɪɟɱɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ
ȼɢɞɧɨ, ɱɬɨ ɧɚɝɪɭɡɤɢ ɜ ɤɚɧɚɥɟ ɭɩɪɚɜɥɟɧɢɹ ɨɛɳɢɦ ɲɚɝɨɦ Ɋɨɲ ɞɨɫɬɢɝɚɸɬ ɦɚɤɫɢɦɚɥɶɧɨɝɨ
ɡɧɚɱɟɧɢɹ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɫɤɨɪɨɫɬɢ ɩɨɥɟɬɚ ɞɨ 200 ɤɦ/ɱ. ɉɪɢ ɷɬɨɦ ɭɫɢɥɢɹ ɜ ɤɚɧɚɥɟ ɩɪɨɞɨɥɶɧɨɝɨ
ɭɩɪɚɜɥɟɧɢɹ Ɋɩɪɨɞ ɫɨɫɬɚɜɥɹɸɬ ɞɨ 80 % ɨɬ ɭɫɢɥɢɹ ɜ ɤɚɧɚɥɟ ɨɛɳɟɝɨ ɲɚɝɚ, ɚ ɜ ɤɚɧɚɥɟ ɩɨɩɟɪɟɱɧɨɝɨ
ɭɩɪɚɜɥɟɧɢɹ Ɋɩɨɩ – ɞɨ 40 %.
ɉɪɨɜɟɞɟɦ ɝɚɪɦɨɧɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɡɚɜɢɫɢɦɨɫɬɢ ɭɫɢɥɢɹ ɜ ɤɚɧɚɥɟ ɨɛɳɟɝɨ ɲɚɝɚ ɩɨ ɚɡɢɦɭɬɭ.
Ⱦɥɹ ɷɬɨɝɨ ɪɚɡɥɨɠɢɦ ɮɭɧɤɰɢɸ Pɨɲ = F (ψ ) ɜ ɪɹɞ Ɏɭɪɶɟ ɧɚ ɢɧɬɟɪɜɚɥɟ ɨɬ 0 ɞɨ 360Û ɢ ɜɵɞɟɥɢɦ ɩɨɫɬɨɹɧɧɭɸ ɢ ɩɟɪɟɦɟɧɧɭɸ ɫɨɫɬɚɜɥɹɸɳɢɟ ɭɫɢɥɢɹ ɩɨ ɤɚɤɨɣ-ɥɢɛɨ ɝɚɪɦɨɧɢɤɟ:
n
Pɨɲ = P0 + ¦ ( Pci cosψ + Psi sinψ ) ,
i =1
ɝɞɟ i – ɧɨɦɟɪ ɝɚɪɦɨɧɢɤɢ.
Ⱥɦɩɥɢɬɭɞɭ ɩɨ ɤɚɤɨɣ-ɥɢɛɨ ɝɚɪɦɨɧɢɤɟ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɩɨ ɮɨɪɦɭɥɟ
ΔPi = Pci2 + Psi2 .
Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɡɚɜɢɫɢɦɨɫɬɢ ɭɫɢɥɢɣ ɜ ɤɚɧɚɥɟ ɨɛɳɟɝɨ ɲɚɝɚ ɨɬ ɫɤɨɪɨɫɬɢ ɩɨɥɟɬɚ ɫɨɩɨɫɬɚɜɥɟɧɵ ɫ ɞɚɧɧɵɦɢ ɥɟɬɧɵɯ ɢɫɩɵɬɚɧɢɣ ɜɟɪɬɨɥɟɬɚ Ɇɢ-34 ɧɚ ɪɢɫ. 9–11.
ɇɚɢɛɨɥɶɲɟɟ ɡɧɚɱɟɧɢɟ ɚɦɩɥɢɬɭɞɵ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɨɬɦɟɱɟɧɨ ɞɥɹ ɩɪɨɯɨɞɧɵɯ
4-ɣ ɢ 8-ɣ ɝɚɪɦɨɧɢɤ, ɤɪɚɬɧɵɯ ɱɢɫɥɭ ɥɨɩɚɫɬɟɣ ɜɢɧɬɚ (ɪɢɫ. 9). ɋɪɚɜɧɟɧɢɟ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɞɥɹ ɩɨɫɬɨɹɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɭɫɢɥɢɹ ɪɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɫɨɝɥɚɫɭɸɬɫɹ ɫ ɞɚɧɧɵɦɢ ɥɟɬɧɵɯ ɢɫɩɵɬɚɧɢɣ (ɪɢɫ. 10). ɉɨ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɭɫɢɥɢɹ ɪɚɫɱɟɬɵ ɞɚɸɬ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɢɟ ɡɧɚɱɟɧɢɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɚɧɧɵɦɢ ɥɟɬɧɵɯ ɢɫɩɵɬɚɧɢɣ (ɪɢɫ. 11), ɱɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɞɨɩɭɳɟɧɢɹɦɢ, ɩɪɢɧɹɬɵɦɢ ɩɪɢ ɪɚɫɱɟɬɟ ɜɨɡɞɭɲɧɵɯ ɧɚɝɪɭɡɨɤ ɧɚ ɥɨɩɚɫɬɹɯ.
Ɋɢɫ. 9. ɋɩɟɤɬɪ ɚɦɩɥɢɬɭɞ
ɭɫɢɥɢɹ ɜ ɤɚɧɚɥɟ ɨɛɳɟɝɨ ɲɚɝɚ
ɞɥɹ V = 200 ɤɦ/ɱ
Ɋɢɫ. 10. ɉɨɫɬɨɹɧɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ
ɭɫɢɥɢɹ ɜ ɤɚɧɚɥɟ ɨɛɳɟɝɨ ɲɚɝɚ
ɧɚ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɚɯ ɩɨɥɟɬɚ
146
Ɋɢɫ. 11. ɉɟɪɟɦɟɧɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ
ɭɫɢɥɢɹ ɜ ɤɚɧɚɥɟ ɨɛɳɟɝɨ ɲɚɝɚ
ɧɚ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɚɯ ɩɨɥɟɬɚ
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
ȼɕȼɈȾɕ
1. Ɋɚɡɪɚɛɨɬɚɧɧɵɣ ɦɟɬɨɞ ɪɚɫɱɟɬɚ ɲɚɪɧɢɪɧɵɯ ɦɨɦɟɧɬɨɜ ɧɚ ɥɨɩɚɫɬɹɯ ɜɢɧɬɚ ɢ ɭɫɢɥɢɣ ɜ ɤɚɧɚɥɚɯ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɜɟɪɬɨɥɟɬɨɦ ɩɨɤɚɡɚɥ ɯɨɪɨɲɟɟ ɫɨɜɩɚɞɟɧɢɟ ɩɨɥɭɱɟɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɫ
ɞɚɧɧɵɦɢ ɥɟɬɧɵɯ ɢɫɩɵɬɚɧɢɣ ɜɟɪɬɨɥɟɬɚ Ɇɢ-34 ɧɚ ɪɟɠɢɦɚɯ ɜɢɫɟɧɢɹ ɢ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɩɨɥɟɬɚ
ɞɥɹ ɩɨɫɬɨɹɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɭɫɢɥɢɹ ɜ ɤɚɧɚɥɚɯ ɨɛɳɟɝɨ ɲɚɝɚ.
2. ɇɟɫɨɜɩɚɞɟɧɢɟ ɪɟɡɭɥɶɬɚɬɨɜ ɞɥɹ ɩɟɪɟɦɟɧɧɨɣ ɱɚɫɬɢ ɭɫɢɥɢɣ ɫɜɹɡɚɧɨ ɫ ɩɪɢɧɹɬɵɦ ɞɨɩɭɳɟɧɢɟɦ ɨ ɩɨɫɬɨɹɧɫɬɜɟ ɢɧɞɭɤɬɢɜɧɨɣ ɫɤɨɪɨɫɬɢ ɩɨ ɞɢɫɤɭ ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ.
3. Ⱦɚɥɶɧɟɣɲɟɟ ɪɚɡɜɢɬɢɟ ɦɟɬɨɞɚ ɪɚɫɱɟɬɚ ɞɨɥɠɧɨ ɛɵɬɶ ɧɚɩɪɚɜɥɟɧɨ ɧɚ ɭɬɨɱɧɟɧɢɟ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɢ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɟɣ ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ ɩɭɬɟɦ ɭɱɟɬɚ:
– ɪɟɚɥɶɧɨɣ ɝɟɨɦɟɬɪɢɢ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɜɢɧɬɨɦ ɢ ɨɫɨɛɟɧɧɨɫɬɟɣ ɤɨɧɫɬɪɭɤɰɢɢ ɪɚɡɥɢɱɧɵɯ ɬɢɩɨɜ ɜɬɭɥɨɤ,
– ɫɨɫɬɚɜɥɹɸɳɢɯ ɲɚɪɧɢɪɧɨɝɨ ɦɨɦɟɧɬɚ ɨɬ ɢɡɝɢɛɧɵɯ ɢ ɤɪɭɬɢɥɶɧɵɯ ɞɟɮɨɪɦɚɰɢɣ
ɥɨɩɚɫɬɢ,
– ɜɵɫɲɢɯ ɝɚɪɦɨɧɢɤ ɦɚɯɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɩɭɬɟɦ ɫɨɜɦɟɫɬɧɨɝɨ ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɣ ɦɚɯɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɥɨɩɚɫɬɢ ɜ ɩɥɨɫɤɨɫɬɢ ɬɹɝɢ ɢ ɩɥɨɫɤɨɫɬɢ ɜɪɚɳɟɧɢɹ,
– ɢɫɬɢɧɧɨɝɨ ɡɚɤɨɧɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɞɭɲɧɨɣ ɧɚɝɪɭɡɤɢ ɩɨ ɞɢɫɤɭ ɜɢɧɬɚ.
ɋɉɂɋɈɄ ɅɂɌȿɊȺɌɍɊɕ
1. Ɇɢɥɶ Ɇ.Ʌ. ȼɟɪɬɨɥɟɬɵ. Ɋɚɫɱɟɬ ɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ. Ɇ.: Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, 1966. Ɍ. 1.
2. Ɏɟɞɭɥɨɜ ȼ.Ⱥ. ɉɪɢɛɥɢɠɟɧɧɵɣ ɦɟɬɨɞ ɩɟɪɟɫɱɟɬɚ ɩɟɪɟɦɟɧɧɨɣ ɱɚɫɬɢ ɲɚɪɧɢɪɧɨɝɨ ɦɨɦɟɧɬɚ ɥɨɩɚɫɬɢ ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ ɜɟɪɬɨɥɟɬɚ // Ɍɪɭɞɵ ɐȺȽɂ. ȼɵɩ. 1373, 1972.
3. Ɇɢɯɟɟɜ Ɋ.Ⱥ. ɉɪɨɱɧɨɫɬɶ ɜɟɪɬɨɥɟɬɨɜ. Ɇ.: Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, 1984.
4. Ⱥɥɝɨɪɢɬɦɵ ɢ ɩɪɨɝɪɚɦɦɵ ɪɚɫɱɟɬɨɜ ɜ ɡɚɞɚɱɚɯ ɞɢɧɚɦɢɤɢ ɜɟɪɬɨɥɟɬɨɜ / ȼ.ɂ. ɒɚɣɞɚɤɨɜ,
ɂ.ɋ. Ɍɪɨɲɢɧ, ɘ.Ɇ. ɂɝɧɚɬɤɢɧ, Ȼ.Ʌ. Ⱥɪɬɚɦɨɧɨɜ. Ɇ.: ɆȺɂ, 1984.
5. ɋɨɯɚɧ Ɉ.ɇ., ɋɤɭɥɤɨɜ Ⱦ.Ⱦ. ɋɬɭɩɢɰɵ ɢ ɥɨɩɚɫɬɢ ɨɫɧɨɜɧɨɝɨ ɢ ɯɜɨɫɬɨɜɨɝɨ ɪɨɬɨɪɨɜ. Ɇ.:
ɆȺɂ, 1985.
6. ɉɚɜɥɟɧɤɨ ɋ.ɇ., Ȼɚɪɢɧɨɜ Ⱥ.ɘ. Ⱥɧɚɥɢɡ ɤɪɭɬɹɳɢɯ ɦɨɦɟɧɬɨɜ, ɫɨɡɞɚɜɚɟɦɵɯ ɥɨɩɚɫɬɹɦɢ
ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ ɢ ɩɨɥɭɱɟɧɧɵɟ ɪɟɡɭɥɶɬɚɬɵ.
7. ɒɚɣɞɚɤɨɜ ȼ.ɂ. Ⱦɢɫɤɨɜɚɹ ɜɢɯɪɟɜɚɹ ɬɟɨɪɢɹ ɧɟɫɭɳɟɝɨ ɜɢɧɬɚ ɫ ɩɨɫɬɨɹɧɧɨɣ ɧɚɝɪɭɡɤɨɣ ɩɨ
ɞɢɫɤɭ // ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ ɜɟɪɬɨɥɟɬɨɜ: ɫɛ. ɧɚɭɱ. ɬɪɭɞɨɜ. ȼɵɩ. 381. Ɇ.: ɆȺɂ, 1976.
CALCULATION OF LOADS ON THE CONTROLS
WITH HELICOPTER MAIN ROTOR OF SINGLE-ROTOR DESIGN
Artamonov B.L., Kruchinin M.M.
The article describes the method of calculation of the moments about the hinge axis of the main rotor hub from the
action of aerodynamic and inertial forces generated on the blade. The assumptions were taken that the blades are absolutely
rigid and have a rectangular shape in plan view. Flapping motion of blade is described accurately up to the first harmonic of
the Fourier series, inductive speed is considered to be uniformly distributed over the rotor disk.
The aerodynamic component of hinge moment is numerical integration of running forces on blade radius taking
into account aerodynamic characteristics of the profiles received according to wind tunnel tests at different angles of attack
and Mach numbers. The moment from elastic forces is determined for the main rotor hub with the lamellar torsion bar. On
the basis of the hinge moments values data loads on rotorcraft rotating ring, arising at different azimuthal location of the
rotating main rotor blades are calculated.
The calculations executed on the example of Mi-34 helicopter main rotor have shown that average loads in one
revolution in the channel of collective pitch control increase in a control path at flying speed. At the same time loads in the
channel of longitudinal control make up to 80 % of loads in the channel of collective pitch control, and in the channel of
lateral control – to 40 % that will well be coordinated with the provided data of flight tests.
Key words: main rotor, hinge moments.
147
ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ
ɋivil Avition High TECHNOLOGIES
Ɍɨɦ 19, ʋ 04, 2016
Vol. 19, ʋ 04, 2016
REFERENCES
1. Mil M.L. Helicopters. Calculation and design. Vol. 1. Moscow: Mashinostroenie, 1966.
2. Fedulov V.A. An approximate method for conversion of the variable part of the hinge moment of main rotor blade of the helicopter. Transactions, TsAGI, Issue 1373, 1972.
3. Mikheev R.A. The strength of the helicopters. Moscow, Mashinostroenie, 1984.
4. Shaidakov V.I., Troshin I.S., Ignatkin Yu.M., Artamonov B.L. The algorithms and calculation programs in helicopter dynamics problems. Moscow: MAI [Moscow Aviation Institute], 1984.
5. Sokhan O.N., Skulkov D.D. Hubs and blades, main and tail rotors. Moscow: MAI [Moscow
Aviation Institute], 1985.
6. Pavlenko N.S., Barinov A.Yu. Analysis of torsional moments produced in main rotor
blades and results obtained. Helicopters forum, 1995.
7. Shaidakov V.I. Disc vortex theory of the main rotor with a constant load on the disk. Collection of scientific works MAI [Moscow Aviation Institute]. Vol. 381. 1976.
ɋȼȿȾȿɇɂə ɈȻ ȺȼɌɈɊȺɏ
Ⱥɪɬɚɦɨɧɨɜ Ȼɨɪɢɫ Ʌɟɣɡɟɪɨɜɢɱ, ɫɬɚɪɲɢɣ ɧɚɭɱɧɵɣ ɫɨɬɪɭɞɧɢɤ, ɤɚɧɞɢɞɚɬ ɬɟɯɧɢɱɟɫɤɢɯ
ɧɚɭɤ, ɡɚɦɟɫɬɢɬɟɥɶ ɡɚɜɟɞɭɸɳɟɝɨ ɤɚɮɟɞɪɨɣ ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ ɜɟɪɬɨɥɟɬɨɜ Ɇɨɫɤɨɜɫɤɨɝɨ ɚɜɢɚɰɢɨɧɧɨɝɨ ɢɧɫɬɢɬɭɬɚ (ɇɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ).
Ʉɪɭɱɢɧɢɧ Ɇɢɯɚɢɥ Ɇɢɯɚɣɥɨɜɢɱ, ɚɫɩɢɪɚɧɬ ɆȺɂ, ɢɧɠɟɧɟɪ-ɤɨɧɫɬɪɭɤɬɨɪ ȺɈ «ɆȼɁ ɢɦ.
Ɇ.Ʌ. Ɇɢɥɹ».
148
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