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Файл:Автоматизация процессов химических производств. Учебное пособие
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Ɉɩɪɟɞɟɥɟɧɢɟ ɞɜɢɠɭɳɟɣ ɫɢɥɵ ɩɨ ɤɚɠɞɨɣ ɢɡ ɮɚɡ:
x
x
y
ɫɪ
ɫɪ
ɝɞɟ
K
y
y
' ɢ
' – ɫɪɟɞɧɢɟ ɞɜɢɠɭɳɢɟ ɫɢɥɵ, ɜ ɮɚɡɚɯ y ɢ x;
ɫɪ
ɫɪ
ɢ K
– ɤɨɷɮɮɢɰɢɟɧɬɵ ɦɚɫɫɨɩɟɪɟɞɚɱɢ ɞɥɹ ɮɚɡ y ɢ x.
x
MKF ', (218)
yy
MKF ', (219)
xx
Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɩɪɨɰɟɫɫɚ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ
ɋɢɫɬɟɦɚ ɫ ɪɟɡɤɢɦ ɜɨɡɪɚɫɬɚɧɢɟɦ ɪɚɫɬɜɨɪɢɦɨɫɬɢ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 61.
Ɋɢɫ. 61. ɋɢɫɬɟɦɚ ɫ ɪɟɡɤɢɦ ɜɨɡɪɚɫɬɚɧɢɟɦ ɪɚɫɬɜɨɪɢɦɨɫɬɢ:
c* = f(T) – ɤɪɢɜɚɹ ɪɚɫɬɜɨɪɢɦɨɫɬɢ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɚɹ ɪɚɜɧɨɜɟɫɢɟ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɨɝɨ
ɪɚɫɬɜɨɪɚ ɩɪɢ ɢɡɦɟɧɟɧɢɢ T; ɫ
= f(T) – ɥɢɧɢɹ ɭɫɥɨɜɧɨɣ ɝɪɚɧɢɰɵ ɦɟɬɚɫɬɚɛɢɥɶɧɨɣ ɨɛɥɚɫɬɢ,
ɩ
Ⱥ – ɧɟɭɫɬɨɣɱɢɜɚɹ, ɥɚɛɢɥɶɧɚɹ ɨɛɥɚɫɬɶ ɦɚɫɫɨɜɨɝɨ ɨɛɪɚɡɨɜɚɧɢɹ ɰɟɧɬɪɨɜ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ,
Ȼ – ɨɬɧɨɫɢɬɟɥɶɧɨ ɭɫɬɨɣɱɢɜɚɹ ɦɟɬɚɫɬɚɛɢɥɶɧɚɹ ɨɛɥɚɫɬɶ ɨɛɪɚɡɨɜɚɧɢɹ ɢ ɪɚɫɬɜɨɪɟɧɢɹ
ɤɪɢɫɬɚɥɥɨɜ, ȼ – ɨɛɥɚɫɬɶ ɧɟɧɚɫɵɳɟɧɧɵɯ ɪɚɫɬɜɨɪɨɜ
ɋɢɫɬɟɦɚ ɫ ɩɥɚɜɧɵɦ ɢɡɦɟɧɟɧɢɟɦ ɪɚɫɬɜɨɪɢɦɨɫɬɢ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 62.
Ɋɢɫ. 62. ɋɢɫɬɟɦɚ ɫ ɩɥɚɜɧɵɦ ɢɡɦɟɧɟɧɢɟɦ ɪɚɫɬɜɨɪɢɦɨɫɬɢ
ɉɟɪɟɯɨɞ ɜ ɨɛɥɚɫɬɶ ɩɟɪɟɫɵɳɟɧɧɵɯ ɪɚɫɬɜɨɪɨɜ ɩɪɨɢɫɯɨɞɢɬ ɬɨɥɶɤɨ ɩɪɢ ɡɧɚɱɢɬɟɥɶɧɨɦ ɨɯɥɚɠɞɟɧɢɢ.
ɉɪɢ ɷɬɨɦ ɜɵɞɟɥɹɟɬɫɹ ɧɟɡɧɚɱɢɬɟɥɶɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɬɜɟɪɞɨɣ ɮɚɡɵ.
71
Ɋɟɤɨɦɟɧɞɭɟɦɵɣ ɫɩɨɫɨɛ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ – ɩɨɥɭɱɟɧɢɟ ɫɩ ɭɞɚɥɟɧɢɟɦ ɱɚɫɬɢ
E
R
N
K
N
K
ɪɚɫɬɜɨɪɢɬɟɥɹ ɢɡ ɪɚɫɬɜɨɪɚ.
Ɋɟɤɨɦɟɧɞɭɟɦɵɣ ɦɟɬɨɞ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ – ɜɚɤɭɭɦ-ɤɪɢɫɬɚɥɥɢɡɚɰɢɹ.
ɋɢɫɬɟɦɚ ɫ ɧɟɡɧɚɱɢɬɟɥɶɧɵɦ ɢɡɦɟɧɟɧɢɟɦ ɪɚɫɬɜɨɪɢɦɨɫɬɢ ɩɪɟɞɫɬɚɜɥɟɧɵ
ɧɚ ɪɢɫ. 63.
Ɋɢɫ. 63. ɋɢɫɬɟɦɚ ɫ ɧɟɡɧɚɱɢɬɟɥɶɧɵɦ ɢɡɦɟɧɟɧɢɟɦ ɪɚɫɬɜɨɪɢɦɨɫɬɢ
Ɋɟɤɨɦɟɧɞɭɟɦɵɣ ɫɩɨɫɨɛ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ – ɩɨɥɭɱɟɧɢɟ ɫɩ ɩɭɬɟɦ ɜɵɩɚɪɢɜɚɧɢɹ
ɪɚɫɬɜɨɪɢɬɟɥɹ ɢɡ ɪɚɫɬɜɨɪɚ.
Ɋɟɤɨɦɟɧɞɭɟɦɵɣ ɦɟɬɨɞ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ – ɢɡɨɬɟɪɦɢɱɟɫɤɚɹ ɤɪɢɫɬɚɥɥɢɡɚɰɢɹ.
ɂɡɨɬɟɪɦɢɱɟɫɤɚɹ ɤɪɢɫɬɚɥɥɢɡɚɰɢɹ – ɷɬɨ ɤɪɢɫɬɚɥɥɢɡɚɰɢɹ ɫ ɭɞɚɥɟɧɢɟɦ ɱɚɫɬɢ
ɪɚɫɬɜɨɪɢɬɟɥɹ ɢɫɩɚɪɟɧɢɟɦ ɢɥɢ ɜɵɦɨɪɚɠɢɜɚɧɢɟɦ.
Ʉɢɧɟɬɢɤɚ ɩɪɨɰɟɫɫɚ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ
ɋɤɨɪɨɫɬɶ ɨɛɪɚɡɨɜɚɧɢɹ ɰɟɧɬɪɨɜ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ:
ɝɞɟ
dN
dt
ɲɬ.
ɦɫ
dN
IKCC
,
dt
– ɱɢɫɥɨ ɱɚɫɬɢɰ, ɨɛɪɚɡɭɸɳɢɯɫɹ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ ɜ ɟɞɢɧɢɰɭ
3
()
N
*
ɩ m
ɜɪɟɦɟɧɢ;
N
0
KKe
NN
,
– ɷɧɟɪɝɢɹ ɚɤɬɢɜɚɰɢɢ ɡɚɪɨɞɵɲɟɨɛɪɚɡɨɜɚɧɢɹ, (ɤȾɠ/ɤɝ);
E
N
ɋ
ɢ ɋ* – ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɟɪɟɫɵɳɟɧɧɨɝɨ ɢ ɧɚɫɵɳɟɧɧɨɝɨ ɪɚɫɬɜɨɪɨɜ, (ɤɝ/ɦ3);
ɩ
T
;
0
– ɤɨɧɫɬɚɧɬɵ,
ɲɬ.
33m
ɦɫ(ɤɝ/ɦ )
;
m = 2–4 – ɤɢɧɟɬɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɬɢɩɚ ɤɪɢɫɬɚɥɥɢɡɭɸɳɟɝɨɫɹ
ɜɟɳɟɫɬɜɚ.
72
Ʉɚɱɟɫɬɜɟɧɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɫɤɨɪɨɫɬɢ ɪɨɫɬɚ ɤɪɢɫɬɚɥɥɨɜ
f
f
t
f
E
Ɂɚɜɢɫɢɦɨɫɬɢ ɫɤɨɪɨɫɬɢ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ ɨɬ ɜɪɟɦɟɧɢ ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚ ɪɢɫ. 64.
Ɋɢɫ. 64. Ɂɚɜɢɫɢɦɨɫɬɢ ɫɤɨɪɨɫɬɢ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ ɨɬ ɜɪɟɦɟɧɢ:
dm
1 –
– ɢɧɞɭɤɰɢɨɧɧɵɣ ɩɟɪɢɨɞ, ɬ. ɟ. ɩɟɪɢɨɞ ɩɨɞɜɢɠɧɨɝɨ ɪɚɜɧɨɜɟɫɢɹ ɡɚɪɨɞɵɲɟɣ
t
0–t1
ɫ ɪɚɫɬɜɨɪɨɦ, ɤɪɢɜɚɹ 1 – ɩɪɢ ɛɨɥɶɲɨɣ ɫɬɟɩɟɧɢ ɩɟɪɟɫɵɳɟɧɢɹ ɢɦɟɟɬ ɪɟɡɤɢɣ ɦɚɤɫɢɦɭɦ
ɫɤɨɪɨɫɬɢ ɩɪɨɰɟɫɫɚ ɜ ɦɨɦɟɧɬ t
ɩɨɥɨɝɢɣ ɦɚɤɫɢɦɭɦ ɜ ɬɟɱɟɧɢɟ ɜɪɟɦɟɧɢ t
(,)
Ct
' , 2 –
dt
, ɤɪɢɜɚɹ 2 – ɩɪɢ ɦɚɥɨɣ ɫɬɟɩɟɧɢ ɩɟɪɟɫɵɳɟɧɢɹ ɢɦɟɟɬ
max
1
dm
' ,
dt
(,)
Ct
2
CC'!!',
12
2–t3
Ʉɨɥɢɱɟɫɬɜɟɧɧɵɟ ɨɰɟɧɤɢ ɫɤɨɪɨɫɬɢ ɪɨɫɬɚ ɤɪɢɫɬɚɥɥɨɜ ɧɚ ɨɫɧɨɜɚɧɢɢ ɞɢɮɮɭɡɢɨɧɧɨɣ ɬɟɨɪɢɢ
ɉɪɨɰɟɫɫ ɜɫɬɪɚɢɜɚɧɢɹ ɦɨɥɟɤɭɥ ɜ ɤɪɢɫɬɚɥɥɵ ɢɞɟɬ ɫ ɛɨɥɶɲɨɣ ɫɤɨɪɨɫɬɶɸ, ɢ
ɤɢɧɟɬɢɤɚ ɩɪɨɰɟɫɫɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶɸ ɩɨɞɜɨɞɚ ɜɟɳɟɫɬɜɚ ɤ ɩɨɜɟɪɯɧɨɫɬɢ
ɤɪɢɫɬɚɥɥɚ:
dm
d
ɝɞɟ ȕ – ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɫɫɨɨɬɞɚɱɢ, ɤɝ/ɦ
ɩ
F – ɩɨɜɟɪɯɧɨɫɬɶ ɤɪɢɫɬɚɥɥɚ, ɦ
' *ɋC
, ɤɝ/ɦ3;
2
.
Ⱦɥɹ ɚɩɩɚɪɚɬɨɜ ɫ ɦɟɲɚɥɤɚɦɢ ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɫɫɨɨɬɞɚɱɢ
ɩ)(*
FɋC
E
2
Âɫ;
, (220)
E
ɡɚɜɢɫɢɬ ɨɬ ɫɥɟ-
ɞɭɸɳɢɯ ɩɚɪɚɦɟɬɪɨɜ:
(, , )
ad n
,
ɦ
ɝɞɟ a – ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣ ɪɚɡɦɟɪ ɤɪɢɫɬɚɥɥɚ;
n – ɱɢɫɥɨ ɨɛɨɪɨɬɨɜ ɦɟɲɚɥɤɢ, ɨɛ/ɦɢɧ;
d
– ɞɢɚɦɟɬɪ ɦɟɲɚɥɤɢ, ɦ.
ɦ
ɉɪɨɰɟɫɫ ɩɨɞɜɨɞɚ ɜɟɳɟɫɬɜɚ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɤɪɢɫɬɚɥɥɚ ɢɞɟɬ ɫ ɛɨɥɶɲɨɣ ɫɤɨɪɨɫɬɶɸ. Ʉɢɧɟɬɢɤɚ ɩɪɨɰɟɫɫɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶɸ ɜɫɬɪɚɢɜɚɧɢɹ ɦɨɥɟɤɭɥ ɜ
ɤɪɢɫɬɚɥɥ:
73
B
K
f
ɝɞɟ
K – ɤɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ ɜɫɬɪɚɢɜɚɧɢɹ ɦɨɥɟɤɭɥ ɜ ɤɪɢɫɬɚɥɥ;
B
dm
dt
B
nɩ
FɋCK
)(*
, (221)
n – ɷɦɩɢɪɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ.
Ɉɛɚ ɩɪɨɰɟɫɫɚ ɩɪɨɬɟɤɚɸɬ ɫ ɫɨɢɡɦɟɪɢɦɵɦɢ ɫɤɨɪɨɫɬɹɦɢ:
ɝɞɟ Ʉ – ɨɛɳɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɫɤɨɪɨɫɬɢ ɩɪɨɰɟɫɫɚ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ:
ɍɱɢɬɵɜɚɹ, ɱɬɨ Ʉ = f (E, KB), ɚ E = f (n), ɜ ɰɟɥɨɦ ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
(,,)
dm
KC ɋ F
, (222)
()
dt
11 1
.
dm
' .
dt
ɩ
E
CFn
*
K
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɤɨɪɨɫɬɶ ɪɨɫɬɚ ɤɪɢɫɬɚɥɥɨɜ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨɜɟɪɯɧɨɫɬɶɸ
ɤɪɢɫɬɚɥɥɚ, ɞɜɢɠɭɳɟɣ ɫɢɥɨɣ ɩɪɨɰɟɫɫɚ ɢ ɫɤɨɪɨɫɬɶɸ ɦɟɲɚɥɤɢ.
Ɉɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ
ɂɡɨɝɢɞɪɢɱɟɫɤɢɣ ɤɪɢɫɬɚɥɥɢɡɚɬɨɪ ɧɟɩɪɟɪɵɜɧɨɝɨ ɞɟɣɫɬɜɢɹ ɫ ɦɟɲɚɥɤɨɣ ɢɡɨɛɪɚɠɟɧ ɧɚ ɪɢɫ. 65.
Ɋɢɫ. 65. ɂɡɨɝɢɞɪɢɱɟɫɤɢɣ ɤɪɢɫɬɚɥɥɢɡɚɬɨɪ ɧɟɩɪɟɪɵɜɧɨɝɨ ɞɟɣɫɬɜɢɹ ɫ ɦɟɲɚɥɤɨɣ
74
ȼ ɫɯɟɦɟ ɩɪɢɧɹɬɨ: Gɫ = G
ɪ
ɦɪ
+ Gɤɪ;
T
=
T
=
T
ɦɪ
= T; ɋɤɪ = 1, ɬ. ɟ. ɤɪɢɫɬɚɥɥɵ
ɤɪ
ɫ
ɱɢɫɬɵɟ.
Ɋɚɛɨɬɚ ɨɛɴɟɤɬɚ
ɂɫɯɨɞɧɵɣ ɝɨɪɹɱɢɣ ɧɚɫɵɳɟɧɧɵɣ ɪɚɫɬɜɨɪ ɩɨɞɚɟɬɫɹ ɫɜɟɪɯɭ ɜ ɚɩɩɚɪɚɬ, ɝɞɟ
ɨɯɥɚɠɞɚɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɯɥɚɞɨɧɨɫɢɬɟɥɹ, ɩɨɞɚɜɚɟɦɨɝɨ ɜ ɪɭɛɚɲɤɭ, ɢ ɫɬɚɧɨɜɢɬɫɹ
ɩɟɪɟɫɵɳɟɧɧɵɦ.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɟɪɟɫɵɳɟɧɢɹ ɪɚɫɬɜɨɪɚ ɢ ɩɪɢ ɢɧɬɟɧɫɢɜɧɨɦ ɩɟɪɟɦɟɲɢɜɚɧɢɢ
ɩɪɨɢɫɯɨɞɢɬ ɤɪɢɫɬɚɥɥɢɡɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɢɡ ɪɚɫɬɜɨɪɚ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ
ɤɪɢɫɬɚɥɥɨɜ (Ɇ
ɉɪɢ ɷɬɨɦ ɤɨɧɰɟɧɬɪɚɰɢɹ ɪɚɫɬɜɨɪɚ ɩɨɧɢɠɚɟɬɫɹ, ɢ ɨɫɬɚɜɲɚɹɫɹ ɠɢɞɤɚɹ ɮɚɡɚ G
ɜ ɫɦɟɫɢ ɫ G
ɉɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ – ɞɢɚɦɟɬɪ ɤɪɢɫɬɚɥɥɨɜ, d
ɐɟɥɶ ɭɩɪɚɜɥɟɧɢɹ ɩɪɨɰɟɫɫɨɦ – ɨɛɟɫɩɟɱɟɧɢɟ d
o Gɤɪ).
ɤɪ
ɜ ɜɢɞɟ ɩɨɬɨɤɚ ɫɭɫɩɟɧɡɢɢ Gc ɜɵɜɨɞɢɬɫɹ ɢɡ ɩɪɨɰɟɫɫɚ.
ɤɪ
= d
ɤɪɡɞ.
ɤɪ
ɦɪ
ɤɪ.
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɜɫɟɦɭ ɜɟɳɟɫɬɜɭ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dh
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
C
SGGG
U
C
dh
. (223)
dt
C
0
:
dt
GG G . (224)
ɪɦɪɤɪ
ɦɪ ɤɪ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɤɪɢɫɬɚɥɥɢɡɭɟɦɨɦɭ ɜɟɳɟɫɬɜɭ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dC
ɦɪ
VGCGCGC
U
ɦɪ ɦɪ ɪ ɧ ɦɪ ɦɪ ɤɪ ɤɪ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
ȼ ɭɪɚɜɧɟɧɢɟ (226) ɩɨɞɫɬɚɜɢɦ ɜɵɪɚɠɟɧɢɟ
ɟɦ ɋ
= 1:
ɤɪ
ɂɡ (227) ɜɵɪɚɡɢɦ G
ɜ ɹɜɧɨɦ ɜɢɞɟ:
ɤɪ
dt
dC
ɦɪ
:
0
dt
ɪ ɧ ɦɪ ɦɪ ɤɪ ɤɪ
GGG ɢɡ (224) ɢ ɩɨɥɚɝɚ-
ɦɪ ɪ ɤɪ
() 0GC G G C G . (227)
ɪɧ ɪɤɪɦɪɤɪ
()
GC C
ɤɪ
ɪɧ ɦɪ
1
C
G
. (228)
ɦɪ
. (225)
0GC G C G C . (226)
75
ȼɵɪɚɠɟɧɢɟ (228) ɩɪɟɞɫɬɚɜɥɹɟɬ Gɤɪ ɧɚ ɨɫɧɨɜɟ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɪɨ-
M
K
E
R
ɰɟɫɫɚ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ.
GM , ɤɨɬɨɪɨɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɚ ɨɫɧɨɜɟ ɮɢɡɢɤɢ ɩɪɨɰɟɫɫɚ ɦɚɫɫɨɩɟ-
ɇɨ
ɤɪ ɤɪ
ɪɟɞɚɱɢ:
3
ɦɫ
T
3
ɲɬ.
dN
ɝɞɟ
ɦɹ
dm
dt
W
ɩɪ
dt
W
ɜ ɨɛɴɟɦɟ Vɫ;
ɩɪ
– ɢɡɦɟɧɟɧɢɟ ɦɚɫɫɵ ɨɞɧɨɝɨ ɤɪɢɫɬɚɥɥɚ ɜ ɟɞ. ɜɪɟɦɟɧɢ, ɤɝ/ɫ.
Ɍɚɤ ɤɚɤ (,)NfC
ɲɬ. ɫɦ
V
ɋ
' ɢ (,)mfCn ' , ɚ ɬɚɤɠɟ
dN dm
VG
, (229)
ɪɩɪɤɪɤɋ
W
dt dt
– ɱɢɫɥɨ ɤɪɢɫɬɚɥɥɨɜ, ɤɨɬɨɪɨɟ ɨɛɪɚɡɭɟɬɫɹ ɡɚ ɜɪɟ-
GM , ɬɨ ɧɚ ɨɫɧɨɜɟ ɮɢ-
ɤɪ ɤɪ
ɡɢɤɢ ɦɚɫɫɨɩɟɪɟɞɚɱɢ ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
(,,)GfCn
' .
ɤɪ
T
ȼ ɰɟɥɨɦ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ:
(,, , ,,)GfGCCCn
'.
ɤɪ ɪ ɧ ɦɪ
T
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɞɥɹ ɪɚɡɦɟɪɚ ɱɚɫɬɢɰ
ɇɚ ɨɫɧɨɜɚɧɢɢ ɞɢɮɮɭɡɢɨɧɧɨɣ ɬɟɨɪɢɢ ɢ ɩɪɚɜɢɥɚ Ɇɚɤ-Ȼɟɧɚ ɫɤɨɪɨɫɬɶ ɪɨɫɬɚ
ɤɪɢɫɬɚɥɥɨɜ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɱɟɪɟɡ ɪɚɞɢɭɫ ɱɚɫɬɢɰ:
dr
K
, (230)
()
dt
*
ɩ n
CC
ɝɞɟ
§·
KK
exp
0
a
¨¸
©¹
; (231)
T
r – ɪɚɞɢɭɫ ɤɪɢɫɬɚɥɥɚ, ɦ;
t – ɜɪɟɦɹ, ɫ;
ɦ
– ɤɨɧɫɬɚɧɬɵ,
Ʉ, Ʉ
0
ɫɤɝ/ɦ
;
n
3
ɋɩ, ɋ* – ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɟɪɟɫɵɳɟɧɧɨɝɨ ɢ ɧɚɫɵɳɟɧɧɨɝɨ ɪɚɫɬɜɨɪɨɜ, ɤɝ/ɦ3;
ȿ
– ɷɧɟɪɝɢɹ ɚɤɬɢɜɚɰɢɢ, ɤȾɠ/ɤɝ;
ɚ
t – ɬɟɦɩɟɪɚɬɭɪɚ, Ʉ;
R – ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ, ɤȾɠ/ɤɝ
ɇɚ ɨɫɧɨɜɚɧɢɢ (230) ɢ (231) – ɞɢɚɦɟɬɪ ɤɪɢɫɬɚɥɥɚ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ:
(,)
dfC
' .
ɤɪ
.
Ʉ.
T
76
ȿɫɥɢ ɩɪɨɰɟɫɫ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ ɜɟɫɬɢ ɩɪɢ T = const =
T
f
= const, ɬɨ ɋ
ɢ ɋ* ɛɭɞɭɬ ɩɪɟɞɨɩɪɟɞɟɥɟɧɵ, ɬ. ɤ. ɫɢɫɬɟɦɚ ɢɦɟɟɬ 2 ɫɬɟɩɟɧɢ ɫɜɨɛɨ-
ɩ
T
ɡɞ
ɞɵ (s = 2).
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, d
ɋ
= const.
ɧ
= d
ɤɪ
ɦɨɠɧɨ ɨɛɟɫɩɟɱɢɬɶ ɫɬɚɛɢɥɢɡɚɰɢɟɣ T ɩɪɢ ɭɫɥɨɜɢɢ
ɤɪɡɞ
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɩɪɨɰɟɫɫɚ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
d
T
VGC GC Gq
UTT
ɋ ɋ ɪ ɪɪ ɪ ɯɥ ɪɯɥ ɯɥ ɤɪ ɤɪ
Ɇɨɠɧɨ ɩɪɢɧɹɬɶ T =
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
ɇɚ ɨɫɧɨɜɚɧɢɢ (227) ɢ (228) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
dt
GC GC GC
ɯɥ ɪɯɥ ɯɥ ɦɪ ɪɦɪ ɦɪ ɤɪ ɪɤɪ ɤɪ
T
=
ɦɪ
d
GC G C G q
ɪɪɪɪ ɯɥɪɯɥɯɥ ɤɪɤɪ
GC G C GC
ɯɥ ɪɯɥ ɯɥ ɦɪ ɪɦɪ ɦɪ ɤɪ ɪɤɪ
ɜɯ ɜɯ
ɜɵɯ
TTT
T
=
T
.
ɤɪ
ɫ
0
:
dt
ɜɯ ɜɯ
TT
ɜɵɯ
TTT
(, , , )
GG G G
T
.
ɪɯɥɦɪɤɪ
. (233)
ɤɪ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ Gɯɥ.
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɤɪɢɫɬɚɥɥɢɡɚɬɨɪɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 66.
ɢ ɨɛɟɫɩɟɱɢɬɶ ɋɧ =
. (232)
Ɋɢɫ. 66. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɤɪɢɫɬɚɥɥɢɡɚɬɨɪɚ
, h
T
Ɉɫɧɨɜɧɵɟ ɪɟɝɭɥɢɪɭɟɦɵɟ ɩɟɪɟɦɟɧɧɵɟ:
ȼɨɡɦɨɠɧɵɟ ɪɟɝɭɥɢɪɭɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ:
ȼɨɡɦɨɠɧɵɟ ɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
77
.
,,GG G.
p ɯɥ c
,
TT
.
ɪɯɥ
ȼɨɡɦɨɠɧɵɟ ɧɟɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
ɪ
,, ,qcc c.
ɤɪ pp pɦɪ ɪɯɥ
ȼ ɰɟɥɨɦ, ɤɪɢɫɬɚɥɥɢɡɚɬɨɪ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɵɦ ɦɧɨɝɨɫɜɹɡɧɵɦ ɨɛɴɟɤɬɨɦ.
Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ
ɪɢɫ. 67.
Ɋɢɫ. 67. Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ
Ɋɟɝɭɥɢɪɨɜɚɧɢɟ:
ɪɟɝɭɥɢɪɨɜɚɧɢɟ T ɜ ɚɩɩɚɪɚɬɟ ɩɨ ɩɨɞɚɱɟ ɯɥɚɞɨɚɝɟɧɬɚ Gɯɥ ɨɛɟɫɩɟɱɢɜɚɟɬ
ɤɨɫɜɟɧɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɩɨɤɚɡɚɬɟɥɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ:
T = f (d
);
ɤɪ
ɪɟɝɭɥɢɪɨɜɚɧɢɟ h ɩɨ ɨɬɛɨɪɭ ɦɚɬɨɱɧɨɝɨ ɪɚɫɬɜɨɪɚ Gɦɪ – ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ
ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɠɢɞɤɨɣ ɮɚɡɟ.
ɋɬɚɛɢɥɢɡɚɰɢɹ ɪɚɫɯɨɞɚ ɢɫɯɨɞɧɨɝɨ ɪɚɫɬɜɨɪɚ G
ɪ – ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɡɚɞɚɧɧɨɣ
ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɭɫɬɚɧɨɜɤɢ.
Ʉɨɧɬɪɨɥɶ:
ɪɚɫɯɨɞɵ:
,,GG G
ɬɟɦɩɟɪɚɬɭɪɵ:
;
ɦɪ ɯɥ
ɜɯ ɜɵɯ ɜɵɯ ɜɯ
,,,,
TTTTT
ɯɥ ɯɥ ɦɪ ɪ
;
ɭɪɨɜɟɧɶ: h.
ɋɢɝɧɚɥɢɡɚɰɢɹ.
Ɂɧɚɱɢɬɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ
78
T
ɨɬ ɡɚɞɚɧɢɹ.
Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ
Ɋɚɜɧɨɜɟɫɢɟ ɜ ɩɪɨɰɟɫɫɟ ɚɛɫɨɪɛɰɢɢ
ɑɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɞɥɹ ɫɢɫɬɟɦɵ ɛɢɧɚɪɧɵɣ ɝɚɡ + ɠɢɞɤɨɫɬɶ:
S = k – f + 2 = 3 – 2 + 2 = 3.
T
ɉɟɪɟɦɟɧɧɵɟ ɞɥɹ ɞɚɧɧɨɣ ɫɢɫɬɟɦɵ: ɬɟɦɩɟɪɚɬɭɪɚ
, ɞɚɜɥɟɧɢɟ Ɋ; ɤɨɧɰɟɧɬɪɚ-
ɰɢɢ ɋ.
T
Ɋɚɜɧɨɜɟɫɢɟ ɬɚɤɨɣ ɫɢɫɬɟɦɵ ɩɪɢ ɩɨɫɬɨɹɧɧɵɯ
ɢ Ɋ ɨɩɢɫɵɜɚɟɬɫɹ ɡɚɤɨɧɨɦ
Ƚɟɧɪɢ:
*
*CmC , (234)
ɝɚ
ɝɞɟ m – ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ:
E
, (235)
m
P
ɝɞɟ ȿ – ɤɨɧɫɬɚɧɬɚ Ƚɟɧɪɢ:
q
E
, (236)
Cln
T
R
ɝɞɟ q – ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɬɟɩɥɨɬɚ ɪɚɫɬɜɨɪɟɧɢɹ;
R – ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ;
ɋ – ɤɨɧɫɬɚɧɬɚ.
ɇɚ ɨɫɧɨɜɚɧɢɢ (235) ɢ (236) ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ m ɡɚɜɢɫɢɬ ɨɬ P ɢ
ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: ɩɪɢ Ɋ
n, mp ; ɩɪɢ Tn, ȿ no mn.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɪɚɫɬɜɨɪɢɦɨɫɬɶ ɝɚɡɚ ɜ ɠɢɞɤɨɫɬɢ ɧɚ ɨɫɧɨɜɚɧɢɢ (236), ɨɩɪɟ-
*
C
ɝ
C
ɞɟɥɹɟɦɚɹ ɤɚɤ:
ɚ
ɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ
ȼɥɢɹɧɢɟ Ɋ ɢ
, ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɞɚɜɥɟɧɢɹ Ɋn ɢ ɭɦɟɧɶɲɟ-
m
T
p.
T
ɧɚ ɫɪɟɞɧɸɸ ɞɜɢɠɭɳɭɸ ɫɢɥɭ ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ (ɪɢɫ. 68)
(ɮɚɡɨɜɵɟ ɞɢɚɝɪɚɦɦɵ ɩɪɢ ɩɪɨɬɢɜɨɬɨɤɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ).
ɉɪɢ Ɋ
1
; 2 – ɩɪɢ Ɋ2 > Ɋ
1
ɫɪ1
1
, ǻ
; 3 – ɩɪɢ
ɫɪ2
T
>
T
, ǻ
3
.
1
ɫɪ3
ɢ
T
, ǻ
Ɋɟɡɭɥɶɬɚɬɵ ɚɧɚɥɢɡɚ ɞɢɚɝɪɚɦɦ:
ǻ
= f (T, Ɋ, ɫɝɧ, ɫɝɤ, ɫɚɧ, ɫɚɤ);
ɫɪ
ǻ
> ǻ
ɫɪ2
ǻ
ɫɪ3
; ɩɪɢ Ɋnĺ ǻɫɪ n;
ɫɪ1
< ǻ
; ɩɪɢ
ɫɪ1
T
nĺ ǻɫɪp.
ȼɥɢɹɧɢɟ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɩɨɬɨɤɨɜ ɧɚ ɫɪɟɞɧɢɟ ɞɜɢɠɭɳɢɟ ɫɢɥɵ ɩɪɨ-
ɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ (ɪɢɫ. 69).
T
79
Ɋɢɫ. 68. ȼɥɢɹɧɢɟ Ɋ ɢ T ɧɚ ɫɪɟɞɧɸɸ ɞɜɢɠɭɳɭɸ ɫɢɥɭ ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ
(ɮɚɡɨɜɵɟ ɞɢɚɝɪɚɦɦɵ ɩɪɢ ɩɪɨɬɢɜɨɬɨɤɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ)
Ɋɢɫ. 69. ȼɥɢɹɧɢɟ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɩɨɬɨɤɨɜ ɧɚ ɫɪɟɞɧɢɟ ɞɜɢɠɭɳɢɟ ɫɢɥɵ
ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ:
1 – ɪɚɛɨɱɚɹ ɥɢɧɢɹ ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ ɩɪɢ ɩɪɨɬɢɜɨɬɨɤɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ,
2 – ɪɚɛɨɱɚɹ ɥɢɧɢɹ ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ ɩɪɢ ɩɪɹɦɨɬɨɤɟ ɪɚɫɩɪɟɞɟɥɹɸɳɢɯ ɜɟɳɟɫɬɜ,
3 – ɪɚɜɧɨɜɟɫɧɚɹ ɥɢɧɢɹ ɩɪɨɰɟɫɫɚ ɚɛɫɨɪɛɰɢɢ
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