Федоров М.П. и др. Информационно-компьютерные технологии в строительстве. Использование программы SCAD для расчета сооружений из плоских элементов
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60
Ƚɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɜ ɜɢɞɟ
0)(
0
xo
u
ɢ
0)(
0
xo
v
ɩɪɢ ɪɚɫɱɟɬɟ
ɬɨɧɤɨɣ ɩɥɢɬɵ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɭɞɨɜɥɟɬɜɨɪɹɸɬɫɹ, ɬɚɤ ɤɚɤ ɛɵɥɨ ɩɪɢɧɹɬɨ
ɞɨɩɭɳɟɧɢɟ ɨ ɬɨɦ, ɱɬɨ ɭɤɚɡɚɧɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɪɚɜɧɵ ɧɭɥɸ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ
ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ. ɉɨɷɬɨɦɭ ɩɪɢ ɪɚɫɱɟɬɟ ɩɪɨɝɢɛɚ ɩɥɢɬɵ ɢɯ ɡɚɩɢɫɵɜɚɬɶ ɧɟ
ɧɭɠɧɨ.
ɇɚ ɲɚɪɧɢɪɧɨ ɩɨɞɜɢɠɧɨɣ ɫɬɨɪɨɧɟ ɨɩɢɪɚɧɢɹ bd ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ,
ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɪɟɲɟɧɢɹ ɨɫɧɨɜɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɪɨɝɢɛɨɜ,
ɡɚɩɢɫɵɜɚɸɬɫɹ ɚɧɚɥɨɝɢɱɧɨ (4.32) – (4.34), ɧɨ ɩɪɢ
1
lx .
Ɂɚɳɟɦɥɟɧɧɵɣ ɤɪɚɣ ɩɥɢɬɵ (ɩɨɥɧɚɹ ɡɚɞɟɥɤɚ). Ɍɚɤɢɦ ɤɪɚɟɦ ɞɥɹ
ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɧɚ ɪɢɫ. 4.2 ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ ɩɥɢɬɵ ɹɜɥɹɟɬɫɹ ɫɬɨɪɨɧɚ cd .
Ɂɞɟɫɶ ɩɪɢ
2
ly
ɩɨ ɜɫɟɣ ɫɬɨɪɨɧɟ ɛɭɞɭɬ ɨɬɫɭɬɫɬɜɨɜɚɬɶ ɩɪɨɝɢɛɵ ɢ ɭɝɥɵ
ɩɨɜɨɪɨɬɚ ɤɚɫɚɬɟɥɶɧɵɯ ɤ ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɣ ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ:
0)(
2
ly
w
(4.35)
.0
2
¸
¸
¹
·
¨
¨
©
§
w
w
ly
y
w
(4.36)
Ʉɪɚɣ ɩɥɢɬɵ ɧɟ ɨɩɟɪɬ (ɫɜɨɛɨɞɟɧ). Ⱦɥɹ ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ ɩɥɢɬɵ,
ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ. 4.2 ɬɚɤɢɦ ɤɪɚɟɦ ɹɜɥɹɟɬɫɹ ɫɬɨɪɨɧɚ ab. ɉɪɢ ɧɟɡɚɝɪɭɠɟɧɧɨɦ
ɢ ɧɟ ɨɩɟɪɬɨɦ ɤɪɚɟ, ɤɚɤ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɩɪɢɦɟɪɟ, ɞɨɥɠɧɵ ɛɵɬɶ ɩɨɫɬɚɜɥɟɧɵ
ɬɪɢ ɭɫɥɨɜɢɹ:
;0)(
0
yy
M
(4.37)
;0)(
0
yy
Q
(4.38)
.0)(
0
yyx
M
(4.39)
Ɉɞɧɚɤɨ, ɤɚɤ ɩɨɤɚɡɵɜɚɟɬ ɚɧɚɥɢɡ, ɤɨɬɨɪɵɣ ɜ ɧɚɲɟɦ ɤɪɚɬɤɨɦ ɩɨɫɨɛɢɢ
ɨɩɭɫɤɚɟɦ, ɧɚ ɛɨɤɨɜɵɯ ɝɪɚɧɹɯ ɩɥɢɬɵ ɦɨɠɧɨ ɫɬɚɜɢɬɶ ɬɨɥɶɤɨ ɞɜɚ ɭɫɥɨɜɢɹ: ɭɫɥɨɜɢɟ
ɪɚɜɟɧɫɬɜɚ ɢɫɤɨɦɨɝɨ ɢɡɝɢɛɚɸɳɟɝɨ ɦɨɦɟɧɬɚ ɡɚɞɚɧɧɨɦɭ ɜɧɟɲɧɟɦɭ ɦɨɦɟɧɬɭ,
ɹɜɥɹɸɳɟɦɭɫɹ ɧɚɝɪɭɡɤɨɣ ɧɚ ɩɥɢɬɭ ɢ ɭɫɥɨɜɢɟ ɧɚ ɤɨɦɛɢɧɚɰɢɸ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɩɨɩɟɪɟɱɧɨɣ ɫɢɥɵ ɢ ɤɪɭɬɹɳɟɝɨ ɦɨɦɟɧɬɚ [7].
ȼ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɩɪɢɦɟɪɟ ɞɥɹ ɝɪɚɧɢɰɵ ab ɩɥɢɬɵ ɩɟɪɜɨɟ ɭɫɥɨɜɢɟ
ɨɫɬɚɟɬɫɹ ɜ ɜɢɞɟ (4.37), ɚ ɜɬɨɪɨɟ ɭɫɥɨɜɢɟ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ
.0)(
0
w
w
y
yx
y
x
M
Q
(4.40)
ɇɚ ɨɫɧɨɜɟ ɩɨɥɭɱɟɧɧɵɯ ɜ ɪɚɡɞɟɥɟ 4 ɭɪɚɜɧɟɧɢɣ ɢ ɮɨɪɦɭɥ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ
ɫɥɟɞɭɸɳɭɸ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ ɇȾɋ ɬɨɧɤɨɣ ɩɥɢɬɵ.
61
1. ɉɪɢ ɡɚɞɚɧɧɨɣ ɧɚɝɪɭɡɤɟ ɧɚ ɩɥɢɬɭ, ɡɚɞɚɧɧɨɣ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɠɟɫɬɤɨɫɬɢ
ɢ ɡɚɞɚɧɧɵɯ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɪɟɲɚɟɬɫɹ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ (4.31)
ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɭɧɤɰɢɹ
),( y
x
ww
ɩɪɨɝɢɛɚ ɩɥɢɬɵ.
2. ɉɨ ɮɨɪɦɭɥɚɦ (4.14) ɢ (4.16) ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɮɭɧɤɰɢɢ
ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ
),( yxMM
xx
ɢ
),( yxMM
yy
, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɵɯ ɩɨ
ɮɨɪɦɭɥɚɦ (4.17), (4.18) ɦɨɠɧɨ ɧɚɣɬɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɧɨɪɦɚɥɶɧɵɟ
ɧɚɩɪɹɠɟɧɢɹ
),,();,,( zyxzyx
yyxx
V
V
V
V
ɢɥɢ (ɩɪɢ 2
/
hz r ) ɢɯ
ɦɚɤɫɢɦɚɥɶɧɵɟ ɱɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ
);,(
2,1,2,1,
yx
xx
V
V
r ).,(
2,1,2,1,
yx
yy
Vr V
3. ɋ ɩɨɦɨɳɶɸ ɮɨɪɦɭɥɵ (4.20) ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɭɧɤɰɢɹ ɤɪɭɬɹɳɟɝɨ ɦɨɦɟɧɬɚ
),( yxMM
xyxy
, ɚ ɩɨ ɧɟɣ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɤɚɫɚɬɟɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ
xy
W
(4.22)
ɢɥɢ ɢɯ ɦɚɤɫɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ (ɩɪɢ 2
/
hz r ).
4. ɉɨ ɮɨɪɦɭɥɚɦ (4.26) ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨɩɟɪɟɱɧɵɟ ɫɢɥɵ ),( yxQQ
xx
ɢ
),( yxQQ
yy
, ɚ ɩɨ ɧɢɦ ɫ ɩɨɦɨɳɶɸ ɮɨɪɦɭɥ (4.28) ɧɚɯɨɞɹɬɫɹ ɦɚɤɫɢɦɚɥɶɧɵɟ
ɡɧɚɱɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɤɚɫɚɬɟɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ
xz
W
ɢ
yz
W
.
Ɉɞɧɚɤɨ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɪɟɲɟɧɢɟ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɜ ɧɟɤɨɬɨɪɵɯ ɩɪɨɫɬɵɯ
ɜɚɪɢɚɧɬɚɯ ɩɥɢɬɵ ɢ ɧɚɝɪɭɡɤɢ [7, 9]. Ɉɛɵɱɧɨ ɡɚɞɚɱɚ ɪɚɫɱɟɬɚ ɩɥɢɬ ɪɟɲɚɟɬɫɹ
ɱɢɫɥɟɧɧɨ ɧɚ ɨɫɧɨɜɟ ɩɪɢɦɟɧɟɧɢɹ ɦɟɬɨɞɚ ɫɟɬɨɤ ɢɥɢ ɆɄɗ.
ȼ ɩɪɨɝɪɚɦɦɧɨɦ ɤɨɦɩɥɟɤɫɟ SCAD ɪɚɫɱɟɬ ɩɥɢɬ ɩɨɫɬɪɨɟɧ ɧɚ ɨɫɧɨɜɟ ɆɄɗ.
ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ Ʉɗ ɞɥɹ ɬɨɧɤɢɯ ɩɥɢɬ, ɩɪɢɦɟɧɹɟɦɵɟ ɜ ɩɪɨɝɪɚɦɦɟ SCAD,
ɩɪɢɜɟɞɟɧɵ ɜ ɫɩɪɚɜɤɟ ɤ ɩɪɨɝɪɚɦɦɟ, ɤɨɬɨɪɚɹ ɥɟɝɤɨ ɞɨɫɬɭɩɧɚ ɞɥɹ ɩɨɥɶɡɨɜɚɬɟɥɹ.
ɇɢɠɟ ɞɥɹ ɨɛɥɟɝɱɟɧɢɹ ɪɚɛɨɬɵ ɫɬɭɞɟɧɬɨɜ ɫ ɩɪɨɝɪɚɦɦɨɣ SCAD ɩɪɢ
ɜɵɩɨɥɧɟɧɢɢ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ ɜ ɤɭɪɫɨɜɵɯ ɪɚɛɨɬɚɯ ɢ ɩɪɨɟɤɬɚɯ ɢɡ ɷɬɨɣ
ɫɩɪɚɜɤɢ ɩɪɢɜɨɞɹɬɫɹ ɧɟɤɨɬɨɪɵɟ ɫɜɟɞɟɧɢɹ.
4.5. Ɍɢɩɵ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɩɪɨɝɪɚɦɦɟ SCAD
ɞɥɹ ɪɚɫɱɟɬɚ ɬɨɧɤɢɯ ɩɥɢɬ
ɋ ɜɨɩɪɨɫɨɦ ɨ ɩɨɥɭɱɟɧɢɢ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɞɥɹ ɬɨɧɤɢɯ ɩɥɢɬ ɩɪɢ
ɪɚɡɥɢɱɧɨɣ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɩɟɪɟɦɟɳɟɧɢɣ ɜɧɭɬɪɢ ɨɛɥɚɫɬɢ ɷɥɟɦɟɧɬɨɜ ɭɱɚɳɢɦɫɹ
ɦɨɠɧɨ ɩɨɡɧɚɤɨɦɢɬɶɫɹ, ɧɚɩɪɢɦɟɪ, ɜ ɪɚɛɨɬɚɯ [8, 9].
ȼ ɞɚɧɧɨɦ ɪɚɡɞɟɥɟ ɩɪɢɜɟɞɟɧ ɬɨɥɶɤɨ ɦɚɬɟɪɢɚɥ ɢɡ ɫɩɪɚɜɤɢ, ɢɦɟɸɳɟɣɫɹ ɜ
ɩɪɨɝɪɚɦɦɟ SCAD. ɗɬɨ ɞɟɥɚɟɬɫɹ ɚɜɬɨɪɚɦɢ ɧɚɫɬɨɹɳɟɝɨ ɍɆɄ ɞɥɹ ɩɨɦɨɳɢ
ɭɱɚɳɢɦɫɹ ɜ ɪɚɫɱɟɬɚɯ ɩɥɢɬ, ɫ ɤɨɬɨɪɵɦɢ ɨɧɢ ɜɫɬɪɟɱɚɸɬɫɹ ɜ ɫɜɨɢɯ ɤɭɪɫɨɜɵɯ
ɢ
ɞɢɩɥɨɦɧɵɯ ɩɪɨɟɤɬɚɯ.
ɉɪɢɜɨɞɢɦɚɹ ɧɢɠɟ ɜ ɪɚɡɞɟɥɟ 4.5 ɧɭɦɟɪɚɰɢɹ ɪɢɫɭɧɤɨɜ ɢ ɨɛɨɡɧɚɱɟɧɢɹ
ɜɟɥɢɱɢɧ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɪɚɡɞɟɥɚɦ 4 ɢ 6 ɫɩɪɚɜɤɢ ɤ ɩɪɨɝɪɚɦɦɟ SCAD.
62
ȿɫɥɢ ɬɨɧɤɚɹ ɩɥɢɬɚ ɪɚɛɨɬɚɟɬ ɬɨɥɶɤɨ ɧɚ ɢɡɝɢɛ, ɬɨ ɞɥɹ ɟɟ ɪɚɫɱɟɬɚ
ɢɫɩɨɥɶɡɭɸɬɫɹ Ʉɗ, ɨɩɢɫɚɧɧɵɟ ɜ ɩɨɞɪɚɡɞɟɥɟ 4.3.3 ɫɩɪɚɜɤɢ. Ⱥ ɟɫɥɢ ɩɥɢɬɚ ɤɪɨɦɟ
ɢɡɝɢɛɚ ɢɫɩɵɬɵɜɚɟɬ ɢ ɩɪɨɞɨɥɶɧɵɟ ɜɨɡɞɟɣɫɬɜɢɹ (ɩɨ ɬɢɩɭ ɛɚɥɤɢ – ɫɬɟɧɤɢ), ɬɨ ɞɥɹ
ɟɟ ɪɚɫɱɟɬɚ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɬɚɤɢɦɢ ɠɟ ɷɥɟɦɟɧɬɚɦɢ, ɤɨɬɨɪɵɟ
ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɪɚɫɱɟɬɚ ɬɨɧɤɢɯ ɩɨɥɨɝɢɯ ɨɛɨɥɨɱɟɤ. ɗɬɢ ɷɥɟɦɟɧɬɵ ɨɩɢɫɚɧɵ ɜ
ɩɨɞɪɚɡɞɟɥɟ
4.3.5 ɫɩɪɚɜɤɢ.
ɉɊɂɅɈɀȿɇɂȿ ɤ ɪɚɡɞɟɥɭ 4 ɍɆɄ
Ɇɚɬɟɪɢɚɥɵ ɢɡ ɫɩɪɚɜɤɢ ɤ ɩɪɨɝɪɚɦɦɟ SCAD
4.3.3. Ɉɩɢɫɚɧɢɟ ɭɧɢɜɟɪɫɚɥɶɧɵɯ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɩɥɢɬɵ
ȼ ɤɨɦɩɥɟɤɫ SCAD ɜɤɥɸɱɟɧɵ ɫɥɟɞɭɸɳɢɟ ɤɨɧɟɱɧɵɟ ɷɥɟɦɟɧɬɵ ɞɥɹ ɪɚɫɱɟɬɚ ɩɥɢɬ:
x ɩɪɹɦɨɭɝɨɥɶɧɵɣ (ɬɢɩ 11 ɢ 13), ɪɢɫɭɧɨɤ 4.10; ɷɥɟɦɟɧɬ 13 ɩɨɥɧɨɫɬɶɸ ɫɨɜɩɚɞɚɟɬ ɫ
ɷɥɟɦɟɧɬɨɦ 11 ɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɩɪɟɟɦɫɬɜɟɧɧɨɫɬɢ ɜɟɪɫɢɢ ɤɨɦɩɥɟɤɫɚ;
x ɬɪɟɭɝɨɥɶɧɵɣ (ɬɢɩ 12 ɢ 14), ɪɢɫɭɧɨɤ 4.11; ɷɥɟɦɟɧɬ 14 ɩɨɥɧɨɫɬɶɸ ɫɨɜɩɚɞɚɟɬ ɫ
ɷɥɟɦɟɧɬɨɦ 12 ɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɩɪɟɟɦɫɬɜɟɧɧɨɫɬɢ ɤɨɦɩɥɟɤɫɚ;
x ɱɟɬɵɪɟɯɭɝɨɥɶɧɵɣ ɱɟɬɵɪɟɯɭɡɥɨɜɨɣ (ɬɢɩ 19), ɪɢɫɭɧɨɤ 4.12;
x ɱɟɬɵɪɟɯɭɝɨɥɶɧɵɣ ɫ ɱɢɫɥɨɦ ɭɡɥɨɜ ɨɬ ɱɟɬɵɪɟɯ ɞɨ ɜɨɫɶɦɢ (ɬɢɩ 20), ɪɢɫɭɧɨɤ 4.13.
Ʉɪɨɦɟ ɜɟɪɲɢɧ ɱɟɬɵɪɟɯɭɝɨɥɶɧɢɤɚ, ɧɚ ɤɚɠɞɨɣ ɢɡ ɫɬɨɪɨɧ ɦɨɠɟɬ ɧɚɯɨɞɢɬɶɫɹ ɩɨ
ɨɞɧɨɦɭ ɭɡɥɭ. ɇɭɦɟɪɚɰɢɹ ɭɡɥɨɜ ɫ 5-ɝɨ ɩɨ 8-ɨɣ ɩɪɨɢɡɜɨɥɶɧɚɹ.
ɉɨɪɹɞɨɤ ɡɚɞɚɧɢɹ ɩɟɪɜɵɯ ɱɟɬɵɪɟɯ (ɬɪɟɯ) ɭɡɥɨɜ ɷɥɟɦɟɧɬɨɜ ɜ ɞɨɤɭɦɟɧɬɟ ɩɪɢɜɟɞɟɧ ɧɚ
ɪɢɫɭɧɤɚɯ.
ȼɫɟ ɷɥɟɦɟɧɬɵ ɩɥɢɬɵ ɢɦɟɸɬ ɦɟɫɬɧɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ X1OY1, ɜ ɤɨɬɨɪɨɣ ɨɫɶ X1
ɩɪɨɯɨɞɢɬ ɨɬ ɩɟɪɜɨɝɨ ɭɡɥɚ ɤɨ ɜɬɨɪɨɦɭ. Ɉɫɶ Y1 ɥɟɠɢɬ ɜ ɩɥɨɫɤɨɫɬɢ XOY, ɨɪɬɨɝɨɧɚɥɶɧɨ X1 ɢ
ɧɚɩɪɚɜɥɟɧɚ ɜ ɫɬɨɪɨɧɭ ɬɪɟɬɶɟɝɨ ɭɡɥɚ.
ɍɧɢɜɟɪɫɚɥɶɧɵɟ ɤɨɧɟɱɧɵɟ ɷɥɟɦɟɧɬɵ, ɨɩɢɫɚɧɧɵɟ ɜ ɷɬɨɦ ɪɚɡɞɟɥɟ, ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ
ɪɚɫɱɟɬɚ ɬɨɧɤɢɯ ɩɥɢɬ. Ʉɚɠɞɵɣ ɭɡɟɥ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɢɦɟɟɬ ɩɨ ɬɪɢ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ:
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W (w) – ɜɟɪɬɢɤɚɥɶɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ (ɩɪɨɝɢɛ), ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɤɨɬɨɪɨɝɨ
ɫɨɜɩɚɞɚɟɬ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɨɫɢ OZ;
UX – ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ X ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɤɨɬɨɪɨɝɨ
ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɜɪɚɳɟɧɢɹ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ, ɟɫɥɢ ɫɦɨɬɪɟɬɶ ɫ ɤɨɧɰɚ ɨɫɢ,
UY – ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ Y, ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɤɨɬɨɪɨɝɨ
ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɜɪɚɳɟɧɢɹ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ, ɟɫɥɢ ɫɦɨɬɪɟɬɶ ɫ ɤɨɧɰɚ ɨɫɢ;
ɋɬɟɩɟɧɢ ɫɜɨɛɨɞɵ W, UX, UY ɨɬɜɟɱɚɸɬ ɢɡɝɢɛɧɵɦ ɞɟɮɨɪɦɚɰɢɹɦ ɩɥɢɬɵ.
ɍɤɚɡɚɧɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɜɵɱɢɫɥɹɸɬɫɹ ɜ ɨɛɳɟɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ.
ɍɫɢɥɢɹ ɜ ɩɥɢɬɟ ɜɵɱɢɫɥɹɸɬɫɹ ɜ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɷɥɟɦɟɧɬɚ. ȼ ɰɟɧɬɪɟ
ɬɹɠɟɫɬɢ ɷɥɟɦɟɧɬɚ ɢ, ɩɨ ɬɪɟɛɨɜɚɧɢɸ, ɜ ɭɡɥɚɯ ɷɥɟɦɟɧɬɚ ɜɵɱɢɫɥɹɸɬɫɹ ɭɫɢɥɢɹ MX, MY, MXY,
QX, QY, (ɩɪɢ ɧɚɥɢɱɢɢ ɭɩɪɭɝɨɝɨ ɨɫɧɨɜɚɧɢɹ ɟɝɨ ɪɟɚɤɰɢɹ RZ) ɢ ɭɡɥɨɜɵɟ ɪɟɚɤɰɢɢ RZi, RUXi,
RUYi,.
4.3.5. ɍɧɢɜɟɪɫɚɥɶɧɵɟ ɤɨɧɟɱɧɵɟ ɷɥɟɦɟɧɬɵ ɞɥɹ ɪɚɫɱɟɬɚ ɨɛɨɥɨɱɟɤ
ȼ ɤɨɦɩɥɟɤɫ SCAD ɜɤɥɸɱɟɧɵ ɫɥɟɞɭɸɳɢɟ ɤɨɧɟɱɧɵɟ ɷɥɟɦɟɧɬɵ ɞɥɹ ɪɚɫɱɟɬɚ ɨɛɨɥɨɱɟɤ:
x ɩɪɹɦɨɭɝɨɥɶɧɵɣ (ɬɢɩ 41), ɪɢɫ. 4.18;
x ɬɪɟɭɝɨɥɶɧɵɣ (ɬɢɩ 42), ɪɢɫ. 4.19;
x ɱɟɬɵɪɟɯɭɝɨɥɶɧɵɣ (ɬɢɩ 44), ɪɢɫ. 4.20.
x ɱɟɬɵɪɟɯɭɝɨɥɶɧɵɣ ɫ ɱɢɫɥɨɦ ɭɡɥɨɜ ɨɬ ɱɟɬɵɪɟɯ ɞɨ ɜɨɫɶɦɢ (ɬɢɩ 50), ɪɢɫ. 4.21. Ʉɪɨɦɟ
ɜɟɪɲɢɧ ɱɟɬɵɪɟɯɭɝɨɥɶɧɢɤɚ ɧɚ ɤɚɠɞɨɣ ɢɡ ɫɬɨɪɨɧ ɦɨɠɟɬ ɧɚɯɨɞɢɬɶɫɹ ɟɳɟ ɩɨ ɨɞɧɨɦɭ
ɭɡɥɭ. ɇɭɦɟɪɚɰɢɹ ɭɡɥɨɜ ɫ 5-ɝɨ ɩɨ 8-ɣ ɩɪɨɢɡɜɨɥɶɧɚɹ.
ȼɫɟ ɷɥɟɦɟɧɬɵ ɨɛɨɥɨɱɤɢ ɢɦɟɸɬ ɦɟɫɬɧɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ X1Y1Z1, ɜ ɤɨɬɨɪɨɣ ɨɫɶ
X1 ɩɪɨɯɨɞɢɬ ɨɬ ɩɟɪɜɨɝɨ ɭɡɥɚ ɤɨ ɜɬɨɪɨɦɭ, ɨɫɶ Y1 ɥɟɠɢɬ ɜ ɩɥɨɫɤɨɫɬɢ ɷɥɟɦɟɧɬɚ, ɨɪɬɨɝɨɧɚɥɶɧɨ
X1 ɢ ɧɚɩɪɚɜɥɟɧɚ ɜ ɫɬɨɪɨɧɭ ɬɪɟɬɶɟɝɨ ɭɡɥɚ, ɚɨɫɶ Z1 ɨɛɪɚɡɭɟɬ ɫ ɨɫɹɦɢ X1 ɢ Y1 ɩɪɚɜɭɸ ɬɪɨɣɤɭ.
ȼɨ ɜɫɟɯ ɷɥɟɦɟɧɬɚɯ ɨɛɨɥɨɱɤɢ ɧɨɪɦɚɥɶɧɨɟ ɢ ɬɚɧɝɟɧɰɢɚɥɶɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ
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ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɥɢɫɶ ɧɟɡɚɜɢɫɢɦɨ. ɂɫɩɨɥɶɡɨɜɚɥɢɫɶ ɮɭɧɤɰɢɢ ɷɥɟɦɟɧɬɨɜ ɬɚɤɨɣ ɠɟ ɮɨɪɦɵ ɞɥɹ
ɪɚɫɱɟɬɚ ɩɥɢɬ ɢ ɛɚɥɨɤ ɫɬɟɧɨɤ.
ɍɧɢɜɟɪɫɚɥɶɧɵɟ ɤɨɧɟɱɧɵɟ ɷɥɟɦɟɧɬɵ, ɨɩɢɫɚɧɧɵɟ ɜ ɷɬɨɦ ɪɚɡɞɟɥɟ, ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ
ɪɚɫɱɟɬɚ ɬɨɧɤɢɯ ɩɨɥɨɝɢɯ ɨɛɨɥɨɱɟɤ. ɇɨ ɨɧɢ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɢ ɞɥɹ ɪɚɫɱɟɬɚ ɬɨɧɤɢɯ
ɩɥɢɬ. Ʉɚɠɞɵɣ ɭɡɟɥ ɷɬɢɯ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɢɦɟɟɬ ɩɨ ɲɟɫɬɶ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ:
U, V, W – ɥɢɧɟɣɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɩɨ ɨɫɹɦ X, Y ɢ Z;
UX – ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ OX, ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɤɨɬɨɪɨɝɨ
ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɜɪɚɳɟɧɢɹ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ, ɟɫɥɢ ɫɦɨɬɪɟɬɶ ɫ ɤɨɧɰɚ ɨɫɢ;
UY – ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ OY, ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɤɨɬɨɪɨɝɨ
ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɜɪɚɳɟɧɢɹ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ, ɟɫɥɢ ɫɦɨɬɪɟɬɶ ɫ ɤɨɧɰɚ ɨɫɢ;
UZ – ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ OZ.
ɋɬɟɩɟɧɢ ɫɜɨɛɨɞɵ U, V ɨɬɜɟɱɚɸɬ ɦɟɦɛɪɚɧɧɵɦ, ɚ W, UX, UY – ɢɡɝɢɛɧɵɦ
ɞɟɮɨɪɦɚɰɢɹɦ. ɍɝɨɥ ɩɨɜɨɪɨɬɚ UZ ɜ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɷɥɟɦɟɧɬɚ ɜɫɟɝɞɚ ɪɚɜɟɧ ɧɭɥɸ.
Ɉɧ ɜɜɨɞɢɬɫɹ ɞɥɹ ɫɬɵɤɨɜɤɢ ɷɥɟɦɟɧɬɨɜ, ɧɟ ɥɟɠɚɳɢɯ ɜ ɨɞɧɨɣ ɩɥɨɫɤɨɫɬɢ ɢ ɧɟɨɛɯɨɞɢɦ ɞɥɹ
ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɪɚɛɨɬɵ ɤɨɧɫɬɪɭɤɰɢɢ. ɉɟɪɟɦɟɳɟɧɢɹ ɜɵɱɢɫɥɹɸɬɫɹ ɜ ɨɛɳɟɣ ɫɢɫɬɟɦɟ
ɤɨɨɪɞɢɧɚɬ.
ȿɫɥɢ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɫɬɪɨɤɟ ɞɨɤɭɦɟɧɬɚ 3 “ɠɟɫɬɤɨɫɬɢ” ɧɟ ɡɚɞɚɧɚ ɫɢɫɬɟɦɚ
ɤɨɨɪɞɢɧɚɬ ɜɵɞɚɱɢ ɭɫɢɥɢɣ, ɬɨ ɩɨ ɭɦɨɥɱɚɧɢɸ ɭɫɢɥɢɹ ɜɵɱɢɫɥɹɸɬɫɹ ɜ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɟ
ɤɨɨɪɞɢɧɚɬ ɷɥɟɦɟɧɬɚ. ȼ ɰɟɧɬɪɟ ɬɹɠɟɫɬɢ ɷɥɟɦɟɧɬɚ ɢ, ɩɨ ɬɪɟɛɨɜɚɧɢɸ, ɜ ɭɡɥɚɯ ɜɵɱɢɫɥɹɸɬɫɹ
ɭɫɢɥɢɹ NX, NY, TXY, MX, MY, MXY, QX, QY, (ɩɪɢ ɧɚɥɢɱɢɢ ɭɩɪɭɝɨɝɨ ɨɫɧɨɜɚɧɢɹ RZ) ɢ
ɭɡɥɨɜɵɟ ɪɟɚɤɰɢɢ Rxi, Ryi, Rzi, RUXi, RUYi, RUZi.
Ɇɚɬɟɪɢɚɥ ɩɥɚɫɬɢɧɵ ɦɨɠɟɬ ɛɵɬɶ ɢɡɨɬɪɨɩɧɵɦ, ɨɪɬɨɬɪɨɩɧɵɦ ɢɥɢ ɚɧɢɡɨɬɪɨɩɧɵɦ.
Ⱦɨɩɭɫɬɢɦɵɟ ɜɢɞɵ ɦɟɫɬɧɵɯ ɧɚɝɪɭɡɨɤ ɧɚ ɤɨɧɟɱɧɵɟ ɷɥɟɦɟɧɬɵ ɩɥɢɬɵ ɩɪɢɜɟɞɟɧɵ ɜ
ɪɚɡɞɟɥɟ 4.3.2.
4.3.6. Ɋɟɡɭɥɶɬɚɬɵ ɫɱɟɬɚ
ȼ ɪɟɡɭɥɶɬɚɬɟ ɫɱɟɬɚ ɜɵɱɢɫɥɹɸɬɫɹ ɩɟɪɟɦɟɳɟɧɢɹ ɭɡɥɨɜ ɜ ɨɛɳɟɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɚ
ɬɚɤɠɟ ɭɫɢɥɢɹ ɜ ɰɟɧɬɪɚɥɶɧɨɣ ɬɨɱɤɟ (ɰɟɧɬɪ ɬɹɠɟɫɬɢ) ɷɥɟɦɟɧɬɚ ɜ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ
(ɩɨ ɭɦɨɥɱɚɧɢɸ) ɢɥɢ ɜ ɥɸɛɨɣ ɞɪɭɝɨɣ (ɩɨ ɭɫɦɨɬɪɟɧɢɸ ɩɨɥɶɡɨɜɚɬɟɥɹ) ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ,
ɩɨɥɨɠɟɧɢɟ ɤɨɬɨɪɨɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɚɞɚɜɚɟɦɵɦɢ ɜ ɞɨɤɭɦɟɧɬɟ 3 ɞɚɧɧɵɦɢ.
Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɤɚɡɚɧɧɨɝɨ ɜ ɫɬɪɨɤɟ 4 ɞɨɤɭɦɟɧɬɚ 0 ɩɪɢɡɧɚɤɚ ɧɚ ɩɟɱɚɬɶ
ɦɨɝɭɬ ɛɵɬɶ ɜɵɜɟɞɟɧɵ ɬɚɤɠɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɭɡɥɚɯ ɷɥɟɦɟɧɬɚ ɢ ɭɡɥɨɜɵɟ ɪɟɚɤɰɢɢ. ɍɡɥɨɜɵɟ
ɪɟɚɤɰɢɢ ɜɵɞɚɸɬɫɹ ɬɨɥɶɤɨ ɜ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ.
ɉɨɥɨɠɢɬɟɥɶɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɢɦɟɸɬ ɧɚɩɪɚɜɥɟɧɢɹ, ɫɨɜɩɚɞɚɸɳɢɟ ɫ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɜɟɤɬɨɪɨɜ ɛɚɡɢɫɚ (ɩɪɚɜɚɹ ɞɟɤɚɪɬɨɜɚɹ ɫɢɫɬɟɦɚ ɤɨɨɪɞɢɧɚɬ).
ɉɟɪɟɱɟɧɶ ɢ ɩɪɚɜɢɥɚ ɱɬɟɧɢɹ ɭɫɢɥɢɣ ɢ ɭɡɥɨɜɵɯ ɪɟɚɤɰɢɣ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 4.13. ɉɪɢ
ɷɬɨɦ ɪɚɡɦɟɪɧɨɫɬɶ ɞɚɧɚ ɞɥɹ ɫɥɭɱɚɹ ɡɚɞɚɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɠɟɫɬɤɨɫɬɢ, ɤɨɨɪɞɢɧɚɬ ɢ ɧɚɝɪɭɡɨɤ ɜ
ɬɨɧɧɚɯ ɢ ɦɟɬɪɚɯ.
ȼ ɫɥɭɱɚɟ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɞɪɭɝɢɯ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɪɟɡɭɥɶɬɚɬɵ ɫɱɟɬɚ ɛɭɞɭɬ ɩɨɥɭɱɟɧɵ ɜ
ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɜɵɛɪɚɧɧɵɦɢ ɟɞɢɧɢɰɚɦɢ ɢɡɦɟɪɟɧɢɹ.
65
Ɍɚɛɥɢɰɚ 4.13.
ɚ) Ɇɟɦɛɪɚɧɧɵɟ ɧɚɩɪɹɠɟɧɢɹ
Ɍɢɩ
Ʉɗ
ɂɧɞɟɤɫɚɰɢɹ Ɉɩɢɫɚɧɢɟ ɉɪɚɜɢɥɨ ɡɧɚɤɨɜ
21–30
41–50
)(
xx
N
V
ɇɨɪɦɚɥɶɧɨɟ
ɧɚɩɪɹɠɟɧɢɟ,
ɞɟɣɫɬɜɭɸɳɟɟ ɜɞɨɥɶ
ɨɫɢ X1
ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɡɧɚɤ ɫɨɨɬɜɟɬɫɬɜɭɟɬ
ɪɚɫɬɹɠɟɧɢɸ
21–30
41–50
)(
yy
N
V
ɇɨɪɦɚɥɶɧɨɟ
ɧɚɩɪɹɠɟɧɢɟ,
ɞɟɣɫɬɜɭɸɳɟɟ ɜɞɨɥɶ
ɨɫɢ Y1
ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɡɧɚɤ ɫɨɨɬɜɟɬɫɬɜɭɟɬ
ɪɚɫɬɹɠɟɧɢɸ. Ⱦɥɹ ɷɥɟɦɟɧɬɨɜ 21–30 ɜɵɱɢɫɥɹɟɬɫɹ
ɬɨɥɶɤɨ ɞɥɹ ɩɥɨɫɤɨ-ɞɟɮɨɪɦɢɪɨɜɚɧɧɵɯ ɫɢɫɬɟɦ
21–30
)(
zz
N
V
ɇɨɪɦɚɥɶɧɨɟ
ɧɚɩɪɹɠɟɧɢɟ
ɞɟɣɫɬɜɭɸɳɟɟ ɜɞɨɥɶ
ɨɫɢ Z1
ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɡɧɚɤ ɫɨɨɬɜɟɬɫɬɜɭɟɬ
ɪɚɫɬɹɠɟɧɢɸ
41–50
xy
T (
xy
W
)
Cɞɜɢɝɚɸɳɟɟ
ɧɚɩɪɹɠɟɧɢɟ
ɋɞɜɢɝ ɫɟɱɟɧɢɹ, ɩɪɢɧɚɞɥɟɠɚɳɟɝɨ ɤɨɧɰɭ
ɷɥɟɦɟɧɬɚ, ɜ ɧɚɩɪɚɜɥɟɧɢɹɯ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ
ɨɫɹɦ X1 ɢ Y1
21–30
xz
T (
xz
W
)
Cɞɜɢɝɚɸɳɟɟ
ɧɚɩɪɹɠɟɧɢɟ
ɋɞɜɢɝ ɫɟɱɟɧɢɹ, ɩɪɢɧɚɞɥɟɠɚɳɟɝɨ ɤɨɧɰɭ
ɷɥɟɦɟɧɬɚ, ɜ ɧɚɩɪɚɜɥɟɧɢɹɯ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ
ɨɫɹɦ X1 ɢ Z1
ɛ) ɂɡɝɢɛɧɵɟ ɧɚɩɪɹɠɟɧɢɹ (ɭɫɢɥɢɹ)
Ɍɢɩ
Ʉɗ
ɂɧɞɟɤɫɚɰɢɹ Ɉɩɢɫɚɧɢɟ ɉɪɚɜɢɥɨ ɡɧɚɤɨɜ
11–20
41–50
Mx Ɇɨɦɟɧɬ ɞɟɣɫɬɜɭɸɳɢɣ ɧɚ
ɫɟɱɟɧɢɟ, ɨɪɬɨɝɨɧɚɥɶɧɨɟ ɨɫɢ ɏ
ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɦɨɦɟɧɬ ɜɵɡɵɜɚɟɬ
ɪɚɫɬɹɠɟɧɢɟ ɧɢɠɧɟɝɨ (ɨɬɧɨɫɢɬɟɥɶɧɨ
ɨɫɢ Z) ɜɨɥɨɤɧɚ ɫɟɱɟɧɢɹ
My Ɍɨ ɠɟ, ɨɪɬɨɝɨɧɚɥɶɧɨɟ ɨɫɢ Y Ɍɨ ɠɟ
Mxy Ʉɪɭɬɹɳɢɣ ɦɨɦɟɧɬ
(ɞɟɣɫɬɜɭɸɳɢɣ ɜ ɫɟɱɟɧɢɢ,
ɨɪɬɨɝɨɧɚɥɶɧɨɦ ɨɫɢ X1).
ȼɪɚɳɟɧɢɟ ɫɟɱɟɧɢɹ, ɩɪɢɧɚɞɥɟɠɚɳɟɝɨ
ɤɨɧɰɭ ɷɥɟɦɟɧɬɚ, ɩɪɨɬɢɜ ɱɚɫɨɜɨɣ
ɫɬɪɟɥɤɢ, ɟɫɥɢ ɫɦɨɬɪɟɬɶ ɫ ɤɨɧɰɚ ɨɫɢ
X1.
11–20
41–50
Qx ɉɟɪɟɪɟɡɵɜɚɸɳɚɹ ɫɢɥɚ ɜ
ɫɟɱɟɧɢɢ, ɨɪɬɨɝɨɧɚɥɶɧɨɦ ɨɫɢ X
ɉɨɥɨɠɢɬɟɥɶɧɚɹ ɩɟɪɟɪɟɡɵɜɚɸɳɚɹ
ɫɢɥɚ ɞɟɣɫɬɜɭɟɬ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɨɫɢ Z
ɧɚ ɬɨɣ ɱɚɫɬɢ Ʉɗ, ɜ ɤɨɬɨɪɨɣ
66
11–20
41–50
Qy Ɍɨ ɠɟ, ɨɪɬɨɝɨɧɚɥɶɧɨɦ ɨɫɢ Y ɨɬɫɭɬɫɬɜɭɟɬ ɭɡɟɥ 1
11–20
41–50
RZ Ɋɟɚɤɬɢɜɧɵɣ ɨɬɩɨɪ ɝɪɭɧɬɚ ɩɪɢ
ɪɚɫɱɟɬɟ ɩɥɢɬ ɢ ɨɛɨɥɨɱɟɤ ɧɚ
ɭɩɪɭɝɨɦ ɨɫɧɨɜɚɧɢɢ
ɉɨɥɨɠɢɬɟɥɶɧɨɟ ɭɫɢɥɢɟ ɞɟɣɫɬɜɭɟɬ ɩɨ
ɧɚɩɪɚɜɥɟɧɢɸ ɨɫɢ Z(ɡɧɚɤ ɦɢɧɭɫ
ɨɡɧɚɱɚɟɬ, ɱɬɨ ɝɪɭɧɬ ɫɠɚɬ)
ɜ) ɍɡɥɨɜɵɟ ɪɟɚɤɰɢɢ
Ɍɢɩ
Ʉɗ
ɂɧɞɟɤɫɚɰɢɹ Ɉɩɢɫɚɧɢɟ ɉɪɚɜɢɥɨ ɡɧɚɤɨɜ
21–30
41–50
RX Ƚɨɪɢɡɨɧɬɚɥɶɧɨɟ ɭɫɢɥɢɟ ɜ i-ɬɨɦ
ɭɡɥɟ Ʉɗ, ɫɨɜɩɚɞɚɸɳɟɟ ɩɨ
ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ
ɨɫɢ X
ɉɨɥɨɠɢɬɟɥɶɧɨɟ ɭɫɢɥɢɟ ɞɟɣɫɬɜɭɟɬ
ɧɚ i-ɣ ɭɡɟɥ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɨɫɢ X
41–50
23, 24,
27
RY Ƚɨɪɢɡɨɧɬɚɥɶɧɨɟ ɭɫɢɥɢɟ ɜ i-ɬɨɦ
ɭɡɥɟ Ʉɗ, ɫɨɜɩɚɞɚɸɳɟɟ ɩɨ
ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ
ɨɫɢ Y
ɉɨɥɨɠɢɬɟɥɶɧɨɟ ɭɫɢɥɢɟ ɞɟɣɫɬɜɭɟɬ
ɧɚ i-ɣ ɭɡɟɥ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɨɫɢ Y
11–20
21–30
41–50
RZ ȼɟɪɬɢɤɚɥɶɧɨɟ ɭɫɢɥɢɟ ɜ i-ɬɨɦ
ɭɡɥɟ Ʉɗ, ɫɨɜɩɚɞɚɸɳɟɟ ɩɨ
ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ
ɨɫɢ Z
ɉɨɥɨɠɢɬɟɥɶɧɨɟ ɭɫɢɥɢɟ ɞɟɣɫɬɜɭɟɬ
ɧɚ i-ɣ ɭɡɟɥ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɨɫɢ Z
11–20
41–50
RUX Ɋɟɚɤɬɢɜɧɵɣ ɦɨɦɟɧɬ ɜ i-ɬɨɦ ɭɡɥɟ
Ʉɗ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ X
ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɦɨɦɟɧɬ ɞɟɣɫɬɜɭɟɬ
ɧɚ i-ɣ ɭɡɟɥ ɩɪɨɬɢɜ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ,
ɟɫɥɢ ɫɦɨɬɪɟɬɶ ɫ ɤɨɧɰɚ ɨɫɢ X
11–20,
41–50
RUY Ɋɟɚɤɬɢɜɧɵɣ ɦɨɦɟɧɬ ɜ i-ɬɨɦ ɭɡɥɟ
Ʉɗ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ Y
ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɦɨɦɟɧɬ ɞɟɣɫɬɜɭɟɬ
ɧɚ i-ɣ ɭɡɟɥ ɩɪɨɬɢɜ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ,
ɟɫɥɢ ɫɦɨɬɪɟɬɶ ɫ ɤɨɧɰɚ ɨɫɢ Y
6.3.3.6. ɉɨɥɨɠɢɬɟɥɶɧɵɟ ɧɚɩɪɚɜɥɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ ɢ ɭɫɢɥɢɣ ɜ Ʉɗ ɨɛɨɥɨɱɤɢ ɢ
ɩɥɢɬɵ
Ʉɗ ɨɛɨɥɨɱɤɢ ɫɨɜɦɟɳɚɟɬ ɜ ɫɟɛɟ Ʉɗ ɛɚɥɤɢ-ɫɬɟɧɤɢ ɢ
ɩɥɢɬɵ, ɩɨɷɬɨɦɭ ɜɫɟ ɩɨɹɫɧɟɧɢɹ, ɩɪɢɜɟɞɟɧɧɵɟ ɜ ɪɚɡɞɟɥɚɯ
6.3.3.4 ɢ 6.3.3.5 ɫɩɪɚɜɟɞɥɢɜɵ ɢ ɞɥɹ ɧɚɫɬɨɹɳɟɝɨ ɪɚɡɞɟɥɚ.
ɇɚ ɪɢɫ. 6.21 ɩɨɤɚɡɚɧɵ ɩɨɥɨɠɢɬɟɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ,
ɩɟɪɟɪɟɡɵɜɚɸɳɢɟ ɫɢɥɵ ɢ ɜɟɤɬɨɪɵ ɦɨɦɟɧɬɨɜ, ɞɟɣɫɬɜɭɸɳɢɟ
ɩɨ ɝɪɚɧɹɦ ɷɥɟɦɟɧɬɚɪɧɨɝɨ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ, ɜɵɪɟɡɚɧɧɨɝɨ ɜ
ɨɤɪɟɫɬɧɨɫɬɢ ɰɟɧɬɪɚ ɬɹɠɟɫɬɢ Ʉɗ ɨɛɨɥɨɱɤɢ ɢɥɢ ɩɥɢɬɵ.
ɉɪɚɜɢɥɚ ɱɬɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ ɢ ɭɫɢɥɢɣ ɞɥɹ Ʉɗ ɨɛɨɥɨɱɟɤ ɢ
ɩɥɚɫɬɢɧ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 4.13.
Ɋɢɫ. 6.21
67
4.6. ɉɪɢɦɟɪ ɪɚɫɱɟɬɚ ɛɚɥɨɱɧɨɣ ɩɥɢɬɵ
Ⱦɥɹ ɩɨɹɫɧɟɧɢɹ ɩɨɧɹɬɢɹ «ɛɚɥɨɱɧɚɹ ɩɥɢɬɚ» ɨɛɪɚɬɢɦɫɹ ɤ ɡɚɞɚɱɟ ɨ ɩɥɨɫɤɨɦ
ɧɚɩɪɹɠɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɬɟɥ (ɫɦ. ɪɢɫ. 1.9 ɢ ɤ ɧɟɦɭ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɬɟɤɫɬ). ɇɚ ɪɢɫ. 1.9 ɩɨɤɚɡɚɧɨ ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɛɟɫɤɨɧɟɱɧɨ
ɞɥɢɧɧɨɣ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɤɢ ɢ ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɷɩɸɪɵ
ɧɚɝɪɭɡɤɢ ɧɚ ɧɟɟ, ɧɟ ɢɡɦɟɧɹɸɳɟɣ ɫɜɨɢɯ ɩɚɪɚɦɟɬɪɨɜ ɩɨ ɜɫɟɣ ɞɥɢɧɟ ɫɬɟɧɤɢ.
ɇȾɋ ɬɚɤɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɫɨɨɪɭɠɟɧɢɹ ɧɚɡɵɜɚɟɬɫɹ ɩɥɨɫɤɢɦ
ɞɟɮɨɪɦɢɪɨɜɚɧɧɵɦ ɫɨɫɬɨɹɧɢɟɦ. ɉɪɢ ɟɝɨ ɨɩɪɟɞɟɥɟɧɢɢ ɢɡ ɫɬɟɧɤɢ ɞɜɭɦɹ
ɩɨɩɟɪɟɱɧɵɦɢ ɫɟɱɟɧɢɹɦɢ, ɩɪɨɜɟɞɟɧɧɵɦɢ ɧɚ ɪɚɫɫɬɨɹɧɢɢ ɨɞɢɧ ɦɟɬɪ, ɜɵɞɟɥɹɟɬɫɹ
ɷɥɟɦɟɧɬ (ɜɦɟɫɬɟ ɫ ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɧɟɝɨ ɧɚɝɪɭɡɤɨɣ).
Ɋɚɫɱɟɬɧɭɸ ɫɯɟɦɭ ɜɵɞɟɥɟɧɧɨɣ ɫɬɟɧɤɢ ɟɞɢɧɢɱɧɨɣ ɬɨɥɳɢɧɵ ɩɪɟɞɫɬɚɜɥɹɸɬ ɜ
ɜɢɞɟ ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫɬɟɧɵ, ɢɦɟɸɳɟɣ ɤɨɧɮɢɝɭɪɚɰɢɸ ɩɨɩɟɪɟɱɧɨɝɨ
ɫɟɱɟɧɢɹ ɫɬɟɧɤɢ (ɫɦ. ɪɢɫ. 1.9). ɉɨɫɤɨɥɶɤɭ ɬɨɥɳɢɧɚ
b ɜɵɞɟɥɟɧɧɨɣ ɫɬɟɧɤɢ (ɫɦ.
ɪɢɫ. 1.8) ɪɚɜɧɚ ɟɞɢɧɢɰɟ ɞɥɢɧɵ, ɬɨ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɧɚɝɪɭɡɤɢ, ɨɬɧɟɫɟɧɧɚɹ ɤ
ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ ɜɵɞɟɥɟɧɧɨɝɨ ɫɥɨɹ ɫɬɟɧɤɢ ɨɫɬɚɟɬɫɹ ɬɚɤɨɣ ɠɟ, ɤɚɤ ɢ
ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɧɚɝɪɭɡɤɢ ɧɚ ɫɬɟɧɤɭ (ɜ ɩɥɨɫɤɨɦ ɧɚɩɪɹɠɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ ɩɪɢ
1zb ɷɬɢ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɛɵɥɢ ɪɚɡɧɵɦɢ, ɫɦ. ɪɢɫ 1.8).
ȿɫɥɢ ɧɚ ɪɢɫ. 1.9 ɩɪɢɧɹɬɶ ɬɨɥɳɢɧɭ
)( yh ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɤɢ ɩɨɫɬɨɹɧɧɨɣ ɢ
ɜɵɩɨɥɧɢɬɶ ɭɫɥɨɜɢɟ ɞɥɹ ɬɨɧɤɨɣ ɩɥɢɬɵ
5/1/
1
dlh
(ɫɦ. ɩɨɞɪɚɡɞɟɥ 4.1), ɬɨ
ɩɨɞɩɨɪɧɚɹ ɫɬɟɧɤɚ ɛɟɫɤɨɧɟɱɧɨɣ ɞɥɢɧɵ
2
l ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɢ Z (ɫɦ. ɪɢɫ. 1.9)
ɩɪɢɦɟɬ ɜɢɞ ɛɟɫɤɨɧɟɱɧɨ ɞɥɢɧɧɨɣ ɬɨɧɤɨɣ ɩɥɢɬɵ. ȼɵɞɟɥɟɧɧɵɣ ɫɥɨɣ ɷɬɨɣ ɩɥɢɬɵ
ɟɞɢɧɢɱɧɨɣ ɬɨɥɳɢɧɵ ɩɪɢɦɟɬ ɜɢɞ ɬɨɧɤɨɣ ɛɚɥɤɢ – ɤɨɧɫɨɥɢ.
ɉɥɢɬɚ, ɡɚɞɚɱɭ ɨɩɪɟɞɟɥɟɧɢɹ ɇȾɋ ɜ ɤɨɬɨɪɨɣ ɦɨɠɧɨ ɡɚɦɟɧɢɬɶ ɡɚɞɚɱɟɣ
ɨɩɪɟɞɟɥɟɧɢɹ ɇȾɋ ɜ ɛɚɥɤɟ ɟɞɢɧɢɱɧɨɣ ɲɢɪɢɧɵ, ɧɚɡɵɜɚɟɬɫɹ ɛɚɥɨɱɧɨɣ.
ȼ ɪɟɚɥɶɧɵɯ ɫɨɨɪɭɠɟɧɢɹɯ ɞɥɢɧɚ
2
l ɩɥɢɬɵ (ɫɦ. ɪɢɫ. 1.9) ɢɦɟɟɬ ɤɨɧɟɱɧɵɟ
ɪɚɡɦɟɪɵ. ɇɨ ɜ ɩɪɚɤɬɢɤɟ ɪɚɫɱɟɬɨɜ ɧɚ ɞɨɫɬɚɬɨɱɧɨɦ ɭɞɚɥɟɧɢɢ ɨɬ ɤɨɧɰɨɜ ɩɥɢɬɵ ɟɟ
ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɤɚɤ ɛɚɥɨɱɧɭɸ. Ⱦɨɩɭɫɬɢɦɨɫɬɶ ɬɚɤɨɝɨ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɩɨɞɯɨɞɚ
ɞɨɥɠɧɚ ɨɰɟɧɢɜɚɬɶɫɹ ɜ ɤɚɠɞɨɦ ɤɨɧɤɪɟɬɧɨɦ ɫɥɭɱɚɟ.
ɉɪɢɦɟɪ 1.
Ɋɚɫɫɦɨɬɪɢɦ ɪɚɫɱɟɬɧɭɸ ɫɯɟɦɭ ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨ ɬɨɧɤɨɣ ɩɥɢɬɵ, ɢɦɟɸɳɟɣ
ɩɪɹɦɨɭɝɨɥɶɧɭɸ ɮɨɪɦɭ (ɪɢɫ. 4.11). ɋɪɟɞɢɧɧɚɹ ɩɥɨɫɤɨɫɬɶ ɩɥɢɬɵ ɪɚɫɩɨɥɚɝɚɟɬɫɹ ɜ ɩɥɨɫɤɨɫɬɢ
XY
. ȼ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɟɣ
X
ɢ
Y
ɩɥɢɬɚ ɢɦɟɟɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɡɦɟɪɵ 60
2
l ɦɢ 10
1
l ɦ.
ɉɨ ɞɥɢɧɧɵɦ ɫɬɨɪɨɧɚɦ ɩɥɢɬɚ ɠɟɫɬɤɨ ɡɚɳɟɦɥɟɧɚ (ɧɚ ɪɢɫ. 4.11 ɡɚɳɟɦɥɟɧɢɟ ɭɫɥɨɜɧɨ ɩɨɤɚɡɚɧɨ
ɡɚɬɟɦɧɟɧɢɟɦ).
Ȼɭɞɟɦ ɩɨɥɚɝɚɬɶ, ɱɬɨ ɦɚɬɟɪɢɚɥɨɦ ɩɥɢɬɵ ɹɜɥɹɟɬɫɹ ɠɟɥɟɡɨɛɟɬɨɧ ɤɥɚɫɫɚ ȼ25. ȼ ɩɟɪɜɨɦ
ɩɪɢɛɥɢɠɟɧɢɢ ɟɟ ɬɨɥɳɢɧɚ ɫɱɢɬɚɟɬɫɹ ɪɚɜɧɨɣ 25 ɫɦ.
ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɩɥɢɬɚ ɡɚɝɪɭɠɟɧɚ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɧɚɝɪɭɡɤɨɣ
68
ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ
1
z
q
ɤɇ/ɦ
2
, ɧɚɩɪɚɜɥɟɧɧɨɣ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ ɟɟ ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ.
Ɂɚɞɚɧɧɚɹ ɩɥɢɬɚ ɢɦɟɟɬ ɫɨɨɬɧɨɲɟɧɢɟ ɞɥɢɧ ɟɟ ɫɬɨɪɨɧ ɪɚɜɧɨɟ ɲɟɫɬɢ:
6/
12
ll
.
Ɋɚɫɫɦɨɬɪɢɦ ɜɨɡɦɨɠɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ
x
M
ɜ
ɬɚɤɨɣ ɩɥɢɬɟ ɟɟ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɪɚɫɱɟɬɚ ɤɚɤ ɛɚɥɨɱɧɨɣ ɩɥɢɬɵ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɟɟ ɤɨɪɨɬɤɨɣ
ɫɬɨɪɨɧɵ. ɋ ɷɬɨɣ ɰɟɥɶɸ ɩɨɫɬɪɨɢɦ ɷɩɸɪɭ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ
x
M
ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ:
1. Ʉɚɤ ɜ ɛɚɥɤɟ, ɜɵɪɟɡɚɧɧɨɣ ɢɡ ɩɥɢɬɵ ɩɨɩɟɪɟɱɧɵɦɢ ɫɟɱɟɧɢɹɦɢ 1-1 ɢ 2-2, ɪɚɫɩɨɥɨɠɟɧɧɵɦɢ
ɧɚ ɪɚɫɫɬɨɹɧɢɢ 1 ɦ ɞɪɭɝ ɨɬ ɞɪɭɝɚ (ɫɦ. ɪɢɫ. 4.11).
2. Ʉɚɤ ɜ ɩɥɢɬɟ, ɪɚɫɫɱɢɬɚɧɧɨɣ ɆɄɗ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ SCAD.
ɉɨɫɬɪɨɟɧɢɟ ɷɩɸɪɵ M
x
ɩɥɢɬɵ ɤɚɤ ɷɩɸɪɵ M ɜ ɜɵɪɟɡɚɧɧɨɣ ɢɡ ɩɥɢɬɵ ɛɚɥɤɟ
Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɜɵɪɟɡɚɧɧɨɣ ɢɡ ɩɥɢɬɵ ɛɚɥɤɢ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 4.12,ɚ.
ɉɨɫɤɨɥɶɤɭ ɛɚɥɤɚ ɹɜɥɹɟɬɫɹ ɬɚɛɥɢɱɧɨɣ (ɫɦ. ɬɚɛɥ. 2.1 ɜ [5]), ɬɨ ɷɩɸɪɚ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ
M
ɞɥɹ ɧɟɟ ɢɡɜɟɫɬɧɚ (ɪɢɫ. 4.12,ɛ). ɂɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ ɜ ɫɟɱɟɧɢɹɯ ɛɚɥɤɢ, ɫɨɜɩɚɞɚɸɳɢɯ ɫ
ɡɚɳɟɦɥɹɸɳɢɦɢ ɨɩɨɪɚɦɢ, ɢ ɜ ɫɟɱɟɧɢɢ ɩɨ ɫɟɪɟɞɢɧɟ ɩɪɨɥɟɬɚ ɛɚɥɤɢ ɢɡɜɟɫɬɧɵ. Ɉɧɢ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵ 12/
2
lq
z
ɢ 24/
2
lq
z
. ɂɯ ɡɧɚɱɟɧɢɹ ɢ ɡɧɚɤɢ ɩɨ ɩɪɚɜɢɥɭ ɡɧɚɤɨɜ, ɩɪɢɧɹɬɵɯ
ɜ ɫɬɪɨɢɬɟɥɶɧɨɣ ɦɟɯɚɧɢɤɟ [3, 4], ɭɤɚɡɚɧɵ ɞɥɹ ɡɚɞɚɧɧɨɣ ɛɚɥɤɢ ɧɚ ɪɢɫ. 4.12,ɛ.
ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɫɩɨɫɨɛɚ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɢɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ
y
M ɜ ɛɚɥɨɱɧɨɣ ɩɥɢɬɟ ɨɬɫɭɬɫɬɜɭɸɬ (0
y
M ).
10
Ɋɢɫ. 4.11
X
1
1
60
2
2
1ɦ
Y
Ɉɋ-1
Ɉɋ-2
8.33 (8.31)
4.17 (4.19)
ɗɩɸɪɚ ɩɥɢɬɵɛɚɥɤɢ
x
MM #
)ɛ
Ɋɢɫ. 4.12
8.33 (8.31)
z
q
Z
X
)a
69
Ɋɚɫɱɟɬ ɩɥɢɬɵ ɆɄɗ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ SCAD
Ⱦɥɹ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ
x
M ɢ
y
M ɩɥɢɬɵ ɫɨ ɡɧɚɱɟɧɢɹɦɢ, ɩɨɥɭɱɟɧɧɵɦɢ
ɩɪɢɛɥɢɠɟɧɧɵɦ ɪɚɫɱɟɬɨɦ ɩɥɢɬɵ ɤɚɤ ɛɚɥɨɱɧɨɣ, ɜɵɩɨɥɧɢɦ ɪɚɫɱɟɬ ɬɨɧɤɨɣ ɩɥɢɬɵ ɆɄɗ ɫ
ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ SCAD.
ɋ ɷɬɨɣ ɰɟɥɶɸ ɡɚɩɭɫɤɚɟɦ ɧɚ ɉɄ ɩɪɨɝɪɚɦɦɭ SCAD. Ɉɬɤɪɵɜɚɟɦ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ «ɇɨɜɵɣ
ɩɪɨɟɤɬ». Ɂɞɟɫɶ ɩɪɢɜɟɞɟɧɚ ɟɝɨ ɱɚɫɬɶ ɫ ɜɜɟɞɟɧɧɵɦɢ ɞɚɧɧɵɦɢ:
ȼɵɯɨɞɢɦ ɢɡ ɨɤɧɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɬɤɪɨɟɬɫɹ ɩɚɩɤɚ SDATA, ɜ ɤɨɬɨɪɨɣ ɫɨɯɪɚɧɹɟɦ ɮɚɣɥ ɫ
ɧɚɡɧɚɱɟɧɧɵɦ ɢɦɟɧɟɦ «ɩɥɢɬɚ-1». ɉɨɫɥɟ ɫɨɯɪɚɧɟɧɢɹ ɢɦɟɧɢ ɮɚɣɥɚ ɩɨɩɚɞɚɟɦ ɧɚ «Ⱦɟɪɟɜɨ
ɩɪɨɟɤɬɚ» [1, 3, 4, 6]. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɩɥɢɬɵ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɨɬɤɪɵɜɚɟɦ:
«Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ» ɢ «ɋɯɟɦɚ». ɇɚ ɨɬɤɪɵɜɲɟɣɫɹ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɨɣ ɩɚɧɟɥɢ ɜɵɛɢɪɚɟɦ ɤɧɨɩɤɭ
«Ƚɟɧɟɪɚɰɢɹ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɫɟɬɤɢ ɷɥɟɦɟɧɬɨɜ ɧɚ ɩɥɨɫɤɨɫɬɢ». ɉɨɹɜɢɬɫɹ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ
«Ƚɟɧɟɪɚɰɢɹ ɩɥɚɫɬɢɧɱɚɬɨɣ ɫɢɫɬɟɦɵ», ɱɚɫɬɶ ɤɨɬɨɪɨɝɨ ɩɨɤɚɡɚɧɚ ɧɢɠɟ:
ɉɪɢ ɜɵɛɪɚɧɧɨɦ ɜ ɩɪɟɞɵɞɭɳɟɦ ɨɤɧɟ ɬɢɩɟ ɫɯɟɦɵ (ɩɥɢɬɚ) ɜ ɩɨɹɜɢɜɲɟɦɫɹ ɨɤɧɟ ɭɠɟ ɛɭɞɟɬ
ɨɬɦɟɱɟɧ ɬɨɱɤɨɣ ɜɢɞ ɫɬɪɨɹɳɟɣɫɹ ɫɯɟɦɵ: «ɉɥɢɬɚ».
XOY
ɨɛɨɡɧɚɱɚɟɬ ɩɥɨɫɤɨɫɬɶ, ɜ ɤɨɬɨɪɨɣ
ɛɭɞɟɬ ɪɚɫɩɨɥɨɠɟɧɚ ɫɪɟɞɢɧɧɚɹ ɩɥɨɫɤɨɫɬɶ ɩɥɢɬɵ.
ȼ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɜɵɩɨɥɧɹɟɦ ɫɥɟɞɭɸɳɢɟ ɞɟɣɫɬɜɢɹ:
1. ɇɚɠɚɬɢɟɦ ɤɧɨɩɤɢ «Ɍɢɩ ɷɥɟɦɟɧɬɚ» ɨɬɤɪɵɜɚɟɦ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɟ ɨɤɧɨ «ɇɚɡɧɚɱɟɧɢɟ ɬɢɩɚ
ɷɥɟɦɟɧɬɚ» (ɟɝɨ ɜɢɞ ɧɟ ɩɪɢɜɨɞɢɬɫɹ). Ɂɞɟɫɶ ɬɚɤɠɟ ɭɠɟ ɛɭɞɟɬ ɨɬɦɟɱɟɧ ɜɢɞ ɫɯɟɦɵ «ɉɥɢɬɚ». ȼ
ɨɤɧɟ ɭɤɚɡɚɧɵ ɜɫɟ ɬɢɩɵ Ʉɗ, ɤɨɬɨɪɵɟ ɛɵɥɢ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɫɩɪɚɜɨɱɧɨɦ ɦɚɬɟɪɢɚɥɟ,
ɩɪɢɜɟɞɟɧɧɨɦ ɜ ɩɨɞɪɚɡɞɟɥɟ 4.5 ɞɚɧɧɨɝɨ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ ɢɡ ɩɪɨɝɪɚɦɦɵ SCAD. ɉɨɤɚɡɚɧɨ, ɱɬɨ
ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɩɪɢɦɟɪɟ ɜɵɛɪɚɧ Ʉɗ ɬɢɩɚ 11. ɋɯɟɦɚ ɜɵɛɪɚɧɧɨɝɨ Ʉɗ ɢɡɨɛɪɚɠɟɧɚ ɜ ɧɢɠɧɟɣ