Исследование колебаний лопаток и дисков ГТД. Чигрин В.С. - 9 стр.

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ɉɚɪɚɦɟɬɪ k ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɚ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ
ɭɪɚɜɧɟɧɢɹ (1.3) ɫ ɝɪɚɧɢɱɧɵɦɢ ɭɫɥɨɜɢɹɦɢ, ɡɚɞɚɜɚɟɦɵɦɢ ɫɩɨɫɨɛɨɦ ɡɚɤɪɟɩɥɟɧɢɹ
ɥɨɩɚɬɤɢ ɧɚ ɞɢɫɤɟ.
ɇɚɢɛɨɥɟɟ ɬɢɩɢɱɧɵɦ ɤɪɟɩɥɟɧɢɟɦ ɪɚɛɨɱɢɯ ɥɨɩɚɬɨɤ ɹɜɥɹɟɬɫɹ ɠɟɫɬɤɚɹ
ɡɚɞɟɥɤɚ ɤɨɪɧɟɜɨɝɨ ɫɟɱɟɧɢɹ ɢ ɧɟɡɚɤɪɟɩɥɟɧɧɵɣ ɤɨɧɟɰ ɩɟɪɚ ɥɨɩɚɬɤɢ (ɤɨɧɫɨɥɶɧɨɟ
ɤɪɟɩɥɟɧɢɟ). Ⱦɥɹ ɷɬɨɝɨ ɫɥɭɱɚɹ
k
1
= 1,875, k
2
= 4,694, ɞɥɹ ɩɨɫɥɟɞɭɸɳɢɯ – k
n
= (n - 0,5)S. Ʉɜɚɞɪɚɬɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ k
n
ɩɨɤɚɡɵɜɚɸɬ ɫɨɨɬɧɨɲɟɧɢɟ
ɫɨɛɫɬɜɟɧɧɵɯ ɱɚɫɬɨɬ ɤɨɥɟɛɚɧɢɣ ɥɨɩɚɬɤɢ:
p
1
: p
2
: p
3
: p
4
... = 1 : 6,28 : 17,53 : 34,36 ... .
Ⱦɪɭɝɢɦ ɬɢɩɢɱɧɵɦ ɤɪɟɩɥɟɧɢɟɦ ɥɨɩɚɬɤɢ ɹɜɥɹɟɬɫɹ ɲɚɪɧɢɪɧɨɟ. Ⱦɥɹ ɧɟɝɨ
k
1 =
0, k
n
= (n - 0,75) S, n = 2, 3 ... .
Ⱦɥɹ ɬɚɤɨɝɨ ɤɪɟɩɥɟɧɢɹ
p
2
: p
3
: p
4
... = 1 : 3,24 : 6,76 ... .
Ɏɨɪɦɭɥɚ (1.5) ɨɫɬɚɟɬɫɹ ɫɩɪɚɜɟɞɥɢɜɨɣ ɢ ɞɥɹ ɩɥɚɫɬɢɧ ɩɟɪɟɦɟɧɧɨɝɨ ɫɟɱɟɧɢɹ.
ȼɨɩɪɨɫ ɫɜɨɞɢɬɫɹ ɥɢɲɶ ɤ ɫɩɨɫɨɛɭ ɞɨɫɬɚɬɨɱɧɨ ɬɨɱɧɨɝɨ ɩɨɥɭɱɟɧɢɹ ɜɟɥɢɱɢɧɵ
k.
ɂɫɩɵɬɭɟɦɚɹ ɩɥɚɫɬɢɧɚ ɢɦɟɟɬ ɞɥɢɧɭ ɞɨ ɡɚɞɟɥɤɢ l = 295 ɦɦ, ɲɢɪɢɧɭ
b = 69,5
ɦɦ, ɬɨɥɳɢɧɭ h = 2,5 ɦɦ. ɉɥɨɬɧɨɫɬɶ ɦɚɬɟɪɢɚɥɚ ɩɥɚɫɬɢɧɵ ɫɨɫɬɚɜɥɹɟɬ
7800
ɤɝ/ ɦ
3
, ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ ȿ = 1,95 10
5
Ɇɇ/ɦ
2
.
Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɫɟɱɟɧɢɹ ɩɥɚɫɬɢɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɣɬɪɚɥɶɧɨɣ ɨɫɢ ɩɪɢ
ɢɡɝɢɛɟ ɜ ɩɥɨɫɤɨɫɬɢ ɦɢɧɢɦɚɥɶɧɨɣ ɠɟɫɬɤɨɫɬɢ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɨ ɮɨɪɦɭɥɟ
I = b h
3
/ 12,
ɩɥɨɳɚɞɶ ɫɟɱɟɧɢɹ ɩɥɚɫɬɢɧɵ F = b h.
Q+dQ
M+dM
Q
qdx
dx
x
x
l
dx
y
M
Ɋɢɫ. 1.4. Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɧɚɝɪɭɡɨɤ
                                                                                   9
     ɉɚɪɚɦɟɬɪ k ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɚ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ
ɭɪɚɜɧɟɧɢɹ (1.3) ɫ ɝɪɚɧɢɱɧɵɦɢ ɭɫɥɨɜɢɹɦɢ, ɡɚɞɚɜɚɟɦɵɦɢ ɫɩɨɫɨɛɨɦ ɡɚɤɪɟɩɥɟɧɢɹ
ɥɨɩɚɬɤɢ ɧɚ ɞɢɫɤɟ.                                  Q+dQ

   y                                                 qdx
                                                                            M+dM



                                            M
                                                           Q
               x                  dx                                dx
                                                x




                l

                          Ɋɢɫ. 1.4. Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɧɚɝɪɭɡɨɤ

      ɇɚɢɛɨɥɟɟ ɬɢɩɢɱɧɵɦ ɤɪɟɩɥɟɧɢɟɦ ɪɚɛɨɱɢɯ ɥɨɩɚɬɨɤ ɹɜɥɹɟɬɫɹ ɠɟɫɬɤɚɹ
ɡɚɞɟɥɤɚ ɤɨɪɧɟɜɨɝɨ ɫɟɱɟɧɢɹ ɢ ɧɟɡɚɤɪɟɩɥɟɧɧɵɣ ɤɨɧɟɰ ɩɟɪɚ ɥɨɩɚɬɤɢ (ɤɨɧɫɨɥɶɧɨɟ
ɤɪɟɩɥɟɧɢɟ). Ⱦɥɹ ɷɬɨɝɨ ɫɥɭɱɚɹ k1 = 1,875, k2 = 4,694, ɞɥɹ ɩɨɫɥɟɞɭɸɳɢɯ – kn
= (n - 0,5)S. Ʉɜɚɞɪɚɬɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ kn ɩɨɤɚɡɵɜɚɸɬ ɫɨɨɬɧɨɲɟɧɢɟ
ɫɨɛɫɬɜɟɧɧɵɯ ɱɚɫɬɨɬ ɤɨɥɟɛɚɧɢɣ ɥɨɩɚɬɤɢ:
                   p1 : p2 : p3 : p4 ... = 1 : 6,28 : 17,53 : 34,36 ... .
       Ⱦɪɭɝɢɦ ɬɢɩɢɱɧɵɦ ɤɪɟɩɥɟɧɢɟɦ ɥɨɩɚɬɤɢ ɹɜɥɹɟɬɫɹ ɲɚɪɧɢɪɧɨɟ. Ⱦɥɹ ɧɟɝɨ
k1 = 0, kn = (n - 0,75) S, n = 2, 3 ... .
       Ⱦɥɹ ɬɚɤɨɝɨ ɤɪɟɩɥɟɧɢɹ
                         p2 : p3 : p4 ... = 1 : 3,24 : 6,76 ... .
     Ɏɨɪɦɭɥɚ (1.5) ɨɫɬɚɟɬɫɹ ɫɩɪɚɜɟɞɥɢɜɨɣ ɢ ɞɥɹ ɩɥɚɫɬɢɧ ɩɟɪɟɦɟɧɧɨɝɨ ɫɟɱɟɧɢɹ.
ȼɨɩɪɨɫ ɫɜɨɞɢɬɫɹ ɥɢɲɶ ɤ ɫɩɨɫɨɛɭ ɞɨɫɬɚɬɨɱɧɨ ɬɨɱɧɨɝɨ ɩɨɥɭɱɟɧɢɹ ɜɟɥɢɱɢɧɵ k.
     ɂɫɩɵɬɭɟɦɚɹ ɩɥɚɫɬɢɧɚ ɢɦɟɟɬ ɞɥɢɧɭ ɞɨ ɡɚɞɟɥɤɢ l = 295 ɦɦ, ɲɢɪɢɧɭ
b = 69,5 ɦɦ, ɬɨɥɳɢɧɭ h = 2,5 ɦɦ. ɉɥɨɬɧɨɫɬɶ ɦɚɬɟɪɢɚɥɚ ɩɥɚɫɬɢɧɵ ɫɨɫɬɚɜɥɹɟɬ
7800 ɤɝ/ ɦ3, ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ ȿ = 1,95 ˜ 105 Ɇɇ/ɦ2.
     Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɫɟɱɟɧɢɹ ɩɥɚɫɬɢɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɣɬɪɚɥɶɧɨɣ ɨɫɢ ɩɪɢ
ɢɡɝɢɛɟ ɜ ɩɥɨɫɤɨɫɬɢ ɦɢɧɢɦɚɥɶɧɨɣ ɠɟɫɬɤɨɫɬɢ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɨ ɮɨɪɦɭɥɟ
                              I = b h3 / 12,
ɩɥɨɳɚɞɶ ɫɟɱɟɧɢɹ ɩɥɚɫɬɢɧɵ F = b h.

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