Проектирование экструзионных машин с учетом качества резинотехнических изделий: Монография 978-594275-325-2, 978-5-94275-325-2
Рассмотрены основные технологические и конструктивные аспекты проектирования одношнековых машин для переработки полимерн
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Russian Pages 173 Year 2007
- Author / Uploaded
- Соколов М.В.
- Клинков А.С.
- Беляев П.С.
- Однолько В.Г.
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. . . .
, . . , . .
"
,
-1" 2007
621.929.3 710.514 791 : "
" , . . "
"
. .Ш
791 : / . . , , . . , . . .– .:" -1", 2007. – 292 . – 400 . – ISBN 978-5-
. . 94275-325-2.
-
. . , . -
,
-
, ,
,
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621.929.3 710.514
ISBN 978-5-94275-325-2
" 2007
. ., . .,
. ., . ., 2007 -1",
, , ,
. . . . 60 × 84 / 16. 16,97
.
" 107076,
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. .
9.02.2007 400 -1", ., 4 -
392000,
,
, 106, . 14
.
№ 124
(
) .
: , ;
; ;
;
;
-
-
. . , . -
. , -
. .
,
, ,
,
. . (
) . , ,
–
. ,
-
. , ,
–
,
,
. , (
,
)
,
,
. ,
, -
. ; (∆T, ∆P, ω)
;
;
; ( ,
)
; .
-
1. 1.1.
: ,
(
),
,
, . ( 10
. 1.1).
: 8;
,
-
10
.
6.
-
,
10. 5,
.
-
,
6. . ,
,
,
-
,
,
,
.
(
),
1
. ,
,
.
-
, .
,
, ,
,
. . . , ,
. ,
2
18
8
-
-
.
. -
12
50 . 16 13, 1,
, 15,
13, 14 . 8,
. 17.
.
11
.
,
-
. . ,
,
, ,
. ,
,
,
.
-
. 1.1.
:
,
,
,
:
ρ
ρ
t–
, ;
V
; p –
Dρ = −ρ(∇V ) ; Dt
DV = −∇p + ∇τ + ρg ; Dt
/ 3; ∇ –
;
; g –
; η–
, ,
q = k∇T ,
k –
,
⋅ ; τ –
(1.3) (1.4)
; cV – , ; q –
(1.2)
τ = η∆ ,
, ,
(1.1)
DT ∂p = −(∇q ) − AT (∇V ) + (τ / ∇V ) A ; Dt ∂T ρ
; ρ –
D – Dt
V –
-
; ∆ –
,
/( ⋅
/( ⋅
, ); T –
); A –
-
.
(1.1 – 1.4) .
. .
[1]
. ( )
"
" (
: U-
-
).
[2].
,
-
:
τ=µ
n –
,
∂V , ∂n
;
( Re ≤ 1 ),
.
( divV = 0 ),
,
,
.
,
gradP = 0 , ∆V = 0 .
,
-
,
, -
,
, . . (1.1 – 1.4) (
-
). , (1.4)
-
(1.1) . [4],
gradP = 0 )
( .
[5, 6]
,
-
. [7]
,
,
. [8 – 26] .
,
.
,
. 1.2 ,
-
. V = ωD/2,
ω–
,
–1
;D–
, ,
,
. ϕ
, Vx
-
Vl,
Vx = Vcosϕ Vx – .
l.
. 1.2.
Vl – ,
. V, x, ,
V Vl = Vsinϕ
-
,
. .
,
,
,
-
. V
-
. ,
.
-
δ
. ,
,
-
. Vx
-
:
Q = ∫ ∫ V x ∂l∂y hB
(1.5)
00
h, B – (1.2)
, , (1.4)
.
,
, x [33]:
µ–
⋅ .
,
-
∂ 2V x ∂ 2V 1 ∂P ( ) = ( 2x + ), µ ∂x ∂y 2 ∂l
(1.6)
(1.6)
, ,
:
V x (0, y ) = 0 ,
V (l , 0) = 0 , V x (b, y ) = 0 ,
Vx –
V x (l , d ) = V x .
(1.7)
. (1.6)
(1.7)
.
[14, 27]. [8, 29], QL = ∆P –
πDδ 3 m∆P
12cµ cos 2 ϕ
, [12]
, ;m– [31]
,
(1.8) ;
–
-
,
. ,
.
-
, .
,
y.
Vx
,
:
-
∫
Q = Vl ∂y = 0 , d
(1.9)
0
U Vx = y x H (1.10) [34 – 38]
(1.10)
,
.
, ,
y 3 − 2 , H
.
[40] – [41 – 42]
[39] .
. .
.
-
. , . [44 – 47] . ,
,
,
,
-
, .
,
[39, 48
γ&
– 57]
τ,
,
, [25, 58 – 62] ,
[39, 46, 47, 63 – 74] – .
,
-
[10, 75, 76]
[24, 77 – 83]. , -
. , , [23, 25, 35 – 37, 81, 84, 85].
∂υ j
∂υi ∂x j
,
∂xi
,
,
.
[80, 82, 86 – 91]
, ,
, .
[54, 92 – 94]
,
, .
-
. . [25, 58 – 62]
.
, [25, 32, 37]
-
,
,
, ,
. .
, -
(1.1 – 1.4)
µ = µ 0 e −b (T −T0 )
(1.11)
∂w = Qc∂T + Q∂P ,
(1.12)
,
. ,
[14, 38, 77, 98]
.
,
-
, .
-
, . ,
, [65, 74].
. .
[73, 74]
.
-
, , . ,
,
. [93]
,
,
(ϕ, h, D, L, ω, T ,
, (N, Q, ∆P)
, . .).
-
:
τ–
;γ–
1 2 J2 –
[74].
,
1 τ = µ0 J 2 2
; µ0 –
( n −1) 2 γ&
,
(1.13)
–1
,
⋅ n;
dv dv 1 J 2 = x + z , 2 dy dy 2
vz
vx –
2
. [93] -200.
,
,
-
( ) ,
,
,
,
.
[94]
:
(
1. ) 2.
,
v x. , ,
(∇v ) = ∂v x ∂x
3. 4. 5.
+
∂v y ∂y
+
, . . z
∂v z = 0. ∂z
(1.14)
.
,
xy
.
: gx = gy = gz = 0.
(1.15)
6. (1.1 – 1.4). 7. ). 8. B/h ≥ 10. 9.
–
(
-
,
, . .
B/h ≥ 10,
. . ,
10. . . 1.3.
−
,
. 1.4. :
, , N = N1+N2+N3,
2
N1 = (B/h)(4Vx +
Vz2)
m0(V/h)
n–1
z Fz –
,
. 1.3.
; N2 = (Vz/2)Bh∆P –
(1.16) ,
. 1.4.
( ) ( ) –
(
,
; Fz =
1 z
∫ exp RT ( z )∂z
z
E
–
–
. 1.3)
,
;
, N3 = V(V/δ)nm0exp[E/(RT )]× ×ecos(ϕ)z – , ;L– , ; V = ωD/2 – –1 ; m0 – , ⋅ n; n – ;E– , /( ⋅ ); T – , ; –
δ,
; Vz = Vcosϕ; z = L/sinϕ – , / ;ω– , ;R– , ; ∆P –
0
,
; Q2 = Bh F p ∆P 12(V h ) Q = Q1 – Q2,
3
Q1 = Vz/(2Bh) Fg – ;e–
, ; Fg
Fp –
n −1
(1.17) m0 Fz z
–
-
,
1.5). ,
B, h
∂z
. 1.6.
(
.
,
-
z, V : V = Q/BH,
(1.18)
qz = ρ V T,
(1.19)
∂qz/∂z = ρ V (∂T/∂z).
(1.20)
QZ (1.19)
z
:
Fg, Fp
h/B
Fg
. 1.5.
Fp
h/B
q:
γ = V/h,
,
α
q = τ γ& = η γ& 2 . ~ 1 T = z
(1.21) :
∫ T ( z )∂z .
z
(1.22)
0
, .
T =T,
-
q = q = α(T – T ).
:
(1.23)
α = kλ/h.
(1.24)
qzBH + q BH∂z = [qz + (∂qz/∂z) ∂z]BH + q B∂ z + q B∂z.
(1.25)
z 1.
.
: G = m0h /(2Kλ)(V/h) 2
T(z) = T + Gexp[E/(RT)] – (Gexp[E/(RT)] – T
; A = 2KaB/(Qh); a = λ/(ρc); K = αh/λ; V = Q/Bh; a – , ;
–
/( 2⋅° ); λ –
, , 3
/( ⋅° ); T , T
n+1
,
, ;α–
.
+ T )exp(–Az), ,
–
.
/ ;B– -
/( ⋅° ); ρ –
,
(1.26) 2
,
/ .
. 1.6.
T :
T = T + Gexp(E/RT ) × 2.
× (1 + (exp(–Az ) – 1)/(Az )) + (T – T
: T(z) = T
.
.
)(exp(–Az ) – 1)/(Az ). (1.27)
+ GBh/(ρcQ)exp(E/RT )z.
(1.28)
T :
T 3.
.
=T
+ GBh/(ρcQ)exp(E/RT)z /2.
.
(1.29)
: T [95 – 107] -
.
=T
.
.
(1.30)
,
, -
. :
,
, [95]:.
.
,
( )
v p + ( v∇) v = ∇ σ + pf ; t
(1.31)
p + (∇pv ) = 0 , t
(1.32)
v pC p + (v∇ )T = ∇(λ∇T ) + (σ e ) t .
σ
–
(1.33)
e
.
(
),
-
(
).
(
).
,
, ,
.
–
, .
-
σ= M e ,
–
,
(1.34)
-
:
M iklm = µ 0 δ il δ km + µ i (< ni nl > δ km + δ im < nk nl >) +
+ 1 / 5µ 2 (6 < ni nm >< nk nl > − < ni nk >< nl nm >) ,
n –
. µ1
µ2
(1.34)
. ,
.
µ0
(1.34)
,
(1.33)
-
,
-
, ,
. (1.31–1.32),
,
-
-
.
,
v, , :
∫ p
v + (v ∇ )v u − P(∇u ) + M : Def t V
1
V
∀H ∈ L2 (V ) ;
(1.35)
T + ( v ∇)T Ψ + λ∇T ∇Ψ dV = ∫ qΨdS + ∫ α(T − T∞ )dS + t S S
+ ∫ M : Def υ : Def υ ΨdV , −
∫ g ⋅ u dS , ∀u ∈ W2 (V );
p ∫ t + ∇( pv) ⋅HdV = 0 , V
∫ pC p
V
v dV =
−
1
∀Ψ ∈ W21 (V ) .
2
V
,
(1.35),
(1.31 – 1.33). ,
,
, .
,
,
[95]. :
Pk = − K (∇v) , K >> 1 . V
u, v,
,
∫ {M : Defv : ∇v − K (∇v)(∇u )}dV = ∫ gu dS ;
-
(1.36)
S
,
,
. . . , .
, ,
, ,
.
. , ,
-
,
.
, .
, ,
. .
,
,
. -
.
. ,
-
, .
S,
, .
, V
. = ϕ(τ s )
.
, ,
, ,
:
-
τ = µ γ&
* 1n
*v
=µ δ
(τ s )1 n
*ϕ
=µ δ
1 n*
µ* .
*
.
n* .
-
,
,
,
. -
.
, -
, . 0,2
1,0
, ,
.
-
, .
h/w < 0,1
,
, .
,
,
,
,
.
,
. ,
h/w < 0,1
, h/w > 1,1
. , -
.
, -
,
-
. . -
-
,
. .
,
,
-
. : ;
. , [95],
− −
∑ Qi = 0
:
m1
i =1
∑ m2
i =1
∆Pi =
;
∑ µ 0 exp(−bT )Qi1/ n = 0 m2
.
i =1
,
. , ,
-
P0 = Q
1/ n
Q
exp(−bT )[Ei (− B ) − Ei (− B exp(−1 / Q))] ,
,
:
nB ≥ Q * exp(−1 / Q * ) ,
(1.37) (1.38)
*
Q * * 1 1 + n * Q * − exp Q = 0 , Q Ei − exp * − Ei − n n n Q n
P0 , Q , B – ,
. n = 1…3
nB = nb(T0 − Ts ) ≥ 3 .
(1.39)
. , 2-
,
3-
,
.
.
[95] -20
-
-286
, ,
,
-
,
, .
-
-
[95] :
.
. ,
,
.
. -
:
, ,
,
,
-
.
-
. -
-
-
,
. . ,
,
.
,
. ,
,
,
,
. .
-
-
. -
,
,
,
,
. -
, ,
-
. ,
.
, ,
. . .
−
,
[95],
:
,
-
-
,
.
-
-
,
−
−
−
; -
;
,
,
; -
−
; .
,
, −
; (
)
-
, , [95]. [108 – 110]
, -
,
,
-
, . ( ).
,
, .
;
− − −
: – –
,
; ;
-
− −
: –
:
,
.
[108]:
∂p ∂σ yy ∂p ∂τ yz ∂p ∂τ xy = ≡b, = ≡0; = ≡a; ∂z ∂y ∂y ∂y ∂x ∂y
τ xy , τ yz , σ yy –
;
(1.40)
= ( , z) –
,
-
. (1.40),
:
τ xy = ay + a1 ; τ yz = by + b1 ,
a1 , b1 , –
(1.41)
. [109] ,
[110]. γ xy Θ 0 (T ) = .
γ yz Θ 0 (T ) = .
1 A = 2 1 − τ xy + τ 2yz
(
,
)
(
)
2 2 − 1 7,8 1 − τ xy + τ yz − β ; γ& xy , γ& yz – : Θ0 (T ) – ;0< 1) (1.51) n, ϕ , qp
2 (δ / D ) n2 + 2 e k 1 − D
Borland Delphi
(DLL) ϕ = 17,65°.
,
q3 =
(1.51)
n1 = n:
(1 − η0,3 ) − (n3 + 1) h D
-
MathCAD.
-
1 . 3 (0) Fd ε k
3 (0)
3 (1) −
1
qp
: qp = q + q .
(1.53)
(1.53)
.
-
. 1.7. q
q . 1.7. (1.53)
, ,
η0 , η , χ .
,
(1.55), qp (
qp,
z.p
):
Bz , p = (1 + χtgϕ)1/ n ( (1) − (0))1/ n . (
. .):
L =P
h
µ 0 (πDN cos ϕ)1/ n (n + 1)1/ n B z , p
W , = kµ 0, ,
Q
120wL tgϕ qp πDNI
=
Q G t
=
( (πDN / 60)1/ n3 +1 δ1/ n3
P 2 3 [(1 − η0 ) + χtgϕ(1 − η ) − 1] ⋅ 10 . ρp q
1G P 2 120 + [(1 − η0 ) + χtgϕ(1 − η ) − 1] π k ρp q q DN cos ϕI p
(
240 wL tgϕ ) t1 + k t q p πDNI
.
−k t
.
tmax ≈ (18tcp − 7t ( . .
):
(1.57)
/ :
(1.58)
: (1.59)
).
:
11.
(1.56)
e cos ϕL ⋅10 3 .
ti +1 = B / A ,
120wL tgϕ (k − k + 3cp ρ p whε − qp πDNI
(1.55)
. .):
,
(k − k ) ;
B = 555,56
sin ϕ .
W = 2v max P [(1 − η0 ) + χtgϕ(1 − η )] .
:
A = 3cpρp whε +
1+1 / n
(1.54)
.
− 3t
.
)/8 .
(1.60)
γ& p = (πDN (n + 1)) / h . :
τ = (η ( ) ⋅ γ& ) /(1 + C2 ⋅ γ&
. .
2α
(1.61)
.
,
,
(1.62)
,
,
,
, -
, , . [112]
( (
)
[112]
)
.
,
-
. [1, 35]
δ* 1 ln 1 + εδ s 1 + N 21− α , K β
T2 − T1 = α–
α
γ& γ& , µ = µ 0 (T ) 0 ; β – γ& , µ = µ1 exp[− β(T − T1 )] ; K –
,
42 700 ·
δs =
*
–
, L2,0 D0-
,
,
/
;
s
DL2
h22 sin α cos α
=
D 2C 2
h22 sin α cos α
δ* =
0)
:
;
πh23 D sin 2 α πh23 sin 2 α , = 12 L2 12C 2
δ* δ* δ1 + N 21−α = δ 0 1 + 0 N 21−,0α . K K 0
(1.65)
(1.66)
δN 21−α = δ 0 N 21−,0α .
(1.67)
h K = K0 2 h2,0
. 3
(1.68)
, .
K= ,l–
,
K=
; –
,
πd 4 , 128l
πd 3 α , 12l l
d K = K 0 d0 d = d 0 h2 / h2,0 , (1.67)
(1.64)
δ* / K = δ*0 / K 0
,
(1.68)
;l–
-
2,
,
d–
–
–
(1.64), (1.66)
d–
;
.
,
,
3
2π µ1β , I γC P
L2 D=
,
-
3
, (
· )
),
ε= ,
( –1
(°
( )
I–
(1.63)
:
, 3
, . . d/l = const,
α . K = K 0 α0 , α = α 0 h2 / h2,0 , 3
(1.68) [112].
h N 21− α = N 21−,0α 2 h2,0
D0 2 . D 2
(1.69)
DN 2 D0 N 2,0 = h2 h2,0
(1.70)
h2 = h2,0 D / D0
[112]:
(1.71)
N 2 = N 2,0 .
(1.72)
,
, ,
D-
D0-
( ):
-
h2 = h2,0 3 D / D0
N 2 = N 2,0 3 ( D / D0 ) 2 .
(1.73)
(1.74)
, ,
.
,
,
,
,
. ,
D > D0
:
h2,0 3 D / D0 < h2 < h2,0 D / D0 ;
(1.75)
N 2,0 3 ( D / D0 ) 2 < N 2 < N 2,0 . [112]
(1.76)
. ,
.
-
,
-
. [112]
− −
:
L1: ; .
− −
L2: (
); .
[112]
,
-
-
. L1
L2 ,
0
+3 1 ± arccos − + 2πn = 2 cos 3/ 2 − 3 < W > +3 3
τw ,
, ,
(1.106) .
:
[207]
, ,
, (1.107), , (1.110) – (1.113)
−1
];
(1.110)
: (1.111)
3 ,
(1.112)
− − < W > = f τ w .
(1.113) -
,
,
.
-
1.4. , [208].
,
, ,
-
. -
.
. 1.20 [209]
.
. , (
. 1.2). x1 = ϕ0;
:
x2 = h; x3 = D; x4 = L; x5 = ω0.
,
Nu =
(
)
π3 D 3 L 1 + 3 sin 2 ϕ 0 µ 0 ω02 L + × 2 H
dP × π 2 D 2 Hω0 cos ϕ 0 . dz Qu =
ω0 2 2 πD sin ϕ 0 H 3 dP π D H cos ϕ 0 sin ϕ 0 − . 2 dz 12 µ 0
∆Pu =
, −
(1.114 – 1.116) : ,
. 1.20.
dP L dP l= . dz sin ϕ0 dz .
(1.114)
(1.115)
(1.116)
-
f1 (x ) = Q (x ) = a1 x2 sin x1 cos x1 − b1 x23 sin 2 x1 ,
(
−
f 2 (x ) = N (x ) =
a1 =
(1.117)
)
a2 1 + 3 sin 2 x1 + b2 x2 sin x1 cos x1 , x2
(1.118)
π 2 D 2 ω0 ω0 2 2 πD ∆Pu ; b2 = ∆Pu . π D ; a2 = π3 D 3µ 0ω02 L ; b1 = 2 2 12µ 0 L
N(x), Q(x) ( ).
ϕ = x1
,
h = x2
. 1.21) ( : µ 0 = 1000 ⋅ n ; = 1⋅10–3 ; Fg = F p = 0,9 .
Q(x) = 80 ° ; n = 1; ω0 = 1,5
(
N(x)) D = 0,08 ; ∆P = 20
; L = = 0,8 ; δ = 1⋅10–3 (1.117 – 1.118)
,
,
∗
( , f(x),
(
.
, ,
∗
)
,
(
(1.118)
(x1 = ϕ0; x2 = h; x3 = D) Q.
) N(x) (1.118)
(
( (
(1.117). . 1.21).
/
-
,
i = 1, 2, …, k; k –
(90
);
),
x)
Q (1.117).
-
x∗
x .
–1
,
:
ai ≤ xi ≤ bi,
; ai, bi –
xi. ,
(1.119) ,
(1.119)
). h,
Q(x)
. 1.21. N(x)
zi,
xi
-
: zi = ai + (bi – ai) sin2 xi, (1.119) [209]
(1.120) .
,
. ,
: x1, x2, x3, x4. x1
x3 / x4 .
x2
α 3 ≤ x 2 x3 ≤ β 3 , α 4 ≤ x3 x 4 ≤ β 4 .
(1.119),
(1.122) β3 , . .
,
: (1.121) (1.122) x2 / x3
(1.121)
, ,
x2 / x3 (1.117 – 1.118).
-
[210]
. ,
1. N,
Q,
∆p
. T°
, . -
, . 2. ,
h
(
(
~ h • = h1• , ..., hN• K j ( h) =
max σ j (h)
[σ] j
)
T
,
= (h1, h2, …, hn) , ) M(h),
, ,
,
-
.
(
,
:
)
K j (h) − 1 = 0, j = 1, N ,
(1.123)
.
(1.123)
.
-
[ ( ) ]
h j ( p +1) = h j ( p ) + h j ( p ) r0−1 K j h( p ) − 1 ,
p–
; r0 –
,
,
(1.124)
. (1.123), (1.124) –
-
. . M(h), h ∈ D,
:
(1.125) (1.126)
K j ( h) − 1 ≤ 0 ,
K j ( h) − 1 ≤ 0 ,
(1.127)
K j ( h) − 1 ≤ 0 ,
(1.128)
K wj (h) − 1 ≤ 0 M(h) –
;D–
, (1.130)
. (1.125) – (1.130)
–
(
a j ≤ hj ≤ bj
(1.129)
(
).
-68)
∆p
Q ,
∆T (
. (
N* . 1.22,
. 1.23). -
Q
)
.
(
-
).
, ,
.
,
-
,
, . -
( ,
) ,
.
,
.
,
,
,
-
a = 2π/t, t–
.
-
. ,
-
. . ,
. ,
.
⋅105
. 1.22.
N*
Q( , T = 80 °C
∆p = 20
)
⋅105
. 1.23. (
№1
T
N*
Q ) ∆p = 20 , ∆T = 30 °C, T =50 °C, = 80 °C, α = 100 /( 2⋅°C)
,
, -
, ,
,
. .
, D = 45 , ; µ = 0,3; γ = 7,8⋅103 / 3; [σ] = 410 pmax = 50 ;
50
( ) ( )(
~ K h ∗ = 1,0 ; ~ K j h ∗ j = 1,4
47
;
[w] = 100 : ; 35 ≤ h2 ≤ 39 ; 360 ≤ h3 ≤ 500 ; 29 ≤ h1 ≤ 33 36 ≤ h4 ≤ 54 ; 2,7 ≤ h5 ≤ 4,5 .
( )
K
,
~ h1∗ = 32
: .
~ M ∗ = 4,056
.
( )
.
~ K h ∗ = 0,599 ;
~ h5∗ = 3,5
–1
-
hi (i = 1...5)
ε = 0,05
)
: E = 2105
38 ; [K]y = 2,5; [w] = 0,25 ;
.
w
( )
.
~ K h ∗ = 0,933 ;
:
( )
~ h ∗ = 0,485 .
;
~ h2∗ = 38
;
~ K h∗ , ~ h3∗ = 500
-
;
~∗ h4 =
ε
minM(h) = 10–4.
. ~ h1∗ = 31,86
: ~ ~ ; h2∗ = 37,8 ; h3∗ = 495 ~∗ M min = 3,689 . ,
~ ; h5∗ = 3,5
~ ; h4∗ = 45,8
.
10 %
. 31,86
; h2 = D2 = 37,86 ( [210, 211]
1 2, [210] , ; h4 = t = 45,8 ; h5 = e = 35 , ; D2 = 37 ; l0 = 480 ; t = 45 ;e=4
; h3 = l0 = 495 1): D1 = 31
, ( , ,
2): h1 = D1 = 12,5 %. -
.
, 2
1
,
. 1.24.
:
1
h, ,
2, d,
3. ,
q1, a –
-
q2
. 1.25. q1
q2
-
. ,
q1′
q 2′ ,
-
:
q1′ =
1 q1 ; K 2
=
bh12 h22 . 6 L (h1 + h2 )
. 1.24.
(
I-II
.
. 1.26)
. 1.25.
,
,
,
. :
W0 = W ; W = W = ∆,
∆– ,
,
; W0, W , W – :
1 R W0 = Pa − q1d 0 ; 2 Eh0
(1.131)
,
(1.132)
W = (q1d − q2 c ) W =
– ;
;
b–
µ–
, ; h0 –
;
;β=b/ –
2
(1.134)
, d
; R =
(1.133)
[1 − µ + β (1 + µ)].
q2 c
2 (β 2 − 1)
d–
R ; Eh
+d – 2
–
-
,
, ;h –
(1.131)
q1 q1 =
Pa
q2
.
:
R0 R + q2 c h0 h 1 ; R0 R d + 2h0 h
E∆ + PaR R0
[
(1.135)
]
2 R0 h + R 2h0 1 . q2 = 2 R c 1 1 − µ + β − (1 + µ) + h 2 β2 −1
∆ [210, 211]:
q1
β
2 a 1 d 1 l ≤ P − − µ 2 + + 2h0 2h0 2 h0 2
a l2 − P + µ 2 h0 2h0 2
(1.136)
,
-
2 a 1 1 σ2 l P2 − − µ 2 + + 2 − 2h0 2 n h0 2
2 2 + a + µ l 1− l h 2h02 2h02 0 2
2 + 1+ l 2h02
+1 ;
(1.137) σϕ = q2 ≤
σ –
σ n
q1d − q2 c σ ≤ ; h n 2
2 β2 + 1 + 1,8 β + 1 + 1,56 2 β −1 β2 − 1 2
(1.138)
,
(1.139)
; σϕ –
;n – . IV (
. 1.24, 1.25):
. 1.26.
,
,
-
max σ 1 = p
2 2 2a l2 d l a + µ − − + 2 2 d − a 2 d d a − ( ) 2 2 (d − a ) (d − a ) 2 2 1 l +1 + + , (1.140) 2 2 2 (d − a ) 2 2 a 2a l d − +µ + 1 + 2 (d − a )2 d 2 (d − a ) d − a
maxσ
β=
b ; c
–
2
( )
2 2 β2 + 1 a2 β + 1 , + + 1 , 8 1 , 56 c 2 β2 − 1 β2 − 1
=p
, ;d–
, ;c–
;µ– ,
, ;b– , ; –
,
, ;l– (1.140)
[(
) (
,
) ( :
M ( x ) = πρ 2 x12 − a 2 + x22 − x12 + 2 x32 − x22 x = ( 1,
: , −
(1.141)
(
2,
3,
)] .
. (1.141) (1.142)
4),
-
).
:
−
max σ 1 , max σ
(1.143)
max σ 2 ≤ [σ]2;
(1.144)
ai ≤ xi ≤ bi, 2
–
i= 1, 2, 3, 4.
,
,
(1.140) ;ρ–
max σ 1 ≤ [σ]1;
(1.145)
,
(1.141); [σ]1, [σ]2 –
; M(x) –
-
; xi – .
; 30 ≤ 434 ; 25 ≤ 1 ≤ 32 = 2 ⋅ 105 ; µ = 0,3; ρ = 7,8 ⋅ 103 /
2 ≤ 37
; 42
3
≤
3 ≤ 52
.
; [σ]2 = : = 22,5 ; = 150 ; [σ]1 = 566 ;8 ≤ 4 ≤ 15 ; – ; "minMT-LC" [220], , ; 4* = 8 ; 3* = 42 ; 2* = 33,6 : 1* = 25,6 * . min = 0,05
1.5.
, . : ,
, ,
.
, ,
. 50 , ,
-
; .
,
,
.
,
. ,
. ,
,
-
. ,
, .
: 1)
,
P, P=
p –
, G, ;
2) 3)
;D –
πD 2 p , 4
(1.146)
, ;
,
-
,
-
;
4)
. , ,
-
. . 1.27.
[43, 210, 211]. , (
,
,
)
.
y max
R
RA
G+P’
P
l/2 a
l . 1.27.
:
P– G–
; ; P' –
;
RA, RB –
A
B,
1.6.
. (
).
-
,
.
,
,
(
)
[212]. ,
,
,
.
,
,
-
,
x. ,
,
:
= min (0) = 2(m + 1) t, (k )
t–
( k −1)
k-
, (m + 1) (r + 1)
;r=n–m– :
∑ xi(k ) − xr(k+)2 ; r +1 i =1
(1.149)
f(x); T(x) – ,
),
: (1.147) (1.148)
f(x), x∈En, (k) – (x) ≥ 0, x, (k) –
En – ,
,
( p m T(x) = ∑ hi2 ( x) + ∑ ui g i2 ( x) , i = m +1 i =1
,
(1.150)
ui –
,
: ui = 0
gi(x) ≥ 0
ui = 1
gi(x) < 0,
(1.151)
: (k)
,
,
,
f(x) (k ≠ i)
(1.150). (1.149)
i
:
|Kj (xi) − 1| ≤ ε,
ε–
.
( p + 1)
xi
–
;r– .
-
"OPTISCRE" (
[
]
= x i( p ) + x i( p ) r −1 K j (x i( p ))− 1 ,
,
,
]
: (1.152)
. (1.149)
,(
[
. ). (1.149) . -
"ITERA"
-
, . ).
[213]
-
. [214] .
1. ,
, .
–
-
, . 2.
(
) ,
. 3. 4.
( ,
"
"(
).
),
, .
5. ,
(
,
)
.
1.7.
− −
: ; c
−
-
; (
),
−
; (
)
, −
; -
−
; (
),
-
,
−
; (
)
,
. 2.
2.1.
, , ,
. . [74]
. .
,
. .
-
[94]:
1) N = N1 + N2 + N3,
N1 = (B/h)(4Vx2 + Vz2)m0(V/h)n – 1z Fz; N2 = (Vz/2)Bh∆P; Fz = Vcosϕ; z = L/sinϕ; V = ωD/2; 2) Q1 = (Vz/2)(B/h)Fg; Q2 = Bh F ∆P/[12(V/h) : 3
3) )
1 z
∫ exp RT ( z ) ∂z ; N
z
E
3
(2.1)
= V(V/δ)nm0exp[E/(RT )]ecos(ϕ)z ; Vz =
0
Q = Q1 – Q2,
(2.2)
n–1
m0Fzz ];
T(z) = T + Gexp[E/(RT)] – (Gexp[E/(RT)] – T
.
+ T )exp(–Az), (2.3)
G
m0h2/(2Kλ)(V/h)n
=
+
1
;
A
=
2KaB/(Qh);
a
λ/(ρc);
=
K
αh/λ;
=
V = Q/Bh. T : T = T + Gexp(E/RT )(1 + (exp(–Az ) – 1)/(Az )) + + (T – T . )(exp(–Az ) – 1)/(Az );, )
(2.4)
[219] T(z) = T
+ GBh/(ρcQ)exp(E/RT )z.
.
(2.5)
T : T
.
=T
.
+ GBh/(ρcQ)exp(E/RT)z /2;
(2.6)
T
;
(2.7)
E ; RT
(2.8)
) 4)
=T
.
.
η = m0 γ& n −1 exp
5) ) [125, 126, 216 – 222]:
,
,
JB(t ) =
∫ τ[T (t )] –
t*
∂t
; τ[T(t)] –
JB (
i ∂t ∂t ∫ τ[T (t )] = ∑i ∫ τ[T (t )] = 1 , t 0
t*
t
(2.9)
i −1
,
(
-
0
" T(t).
p
); t* –
"
"
p
" p
-
(
)
,
,
: σ ≤ [σ] (
6)
.
( EJ ≤ [EJ], y ≤ [y],
,
)
-
).
2.2.
2.2.1.
(2.1) – (2.9) . . ( 224],
) (
D = 0,032 ,
ϕ = 17 ,
L/D
=
10, h = (0,002…0,005) , δ = 0,001 . ,
. 2.1) [223, -
= 0,0035 ,
,
ω = (0…7,85) ,
, (
-
–1
.
).
-
. , . ;
:
–
N=N
-
= I U ; N xx = I xxU ,
N–
,
, ;I –
-
.
− N xx ; N
,
.
–
,
;N
;N – , ;U–
:
– ,
, ;I –
-
, . "
3, 4, 5, h = (0,003…0,008) , (0…12,56)
–1
.
δ = 0,001
-
"(
. 2.2) [224], D = 0,06 , = 0,006 ,
1, ϕ = 17 ,
ω =
:
α.
2
1 :
N = M 2πn ,
–
, ⋅ ;n–
, 3, 4, 5 (
"
-
,
/c. 1
").
. 2.1. : 1–
;2– ;5–
;3–
;4– ;6– 7–
;
. 2.2. 1–
M
;2–
= P r sin α ,
P–
(
, ;r–
. 2.2,
):
, .
N =M ϕ,
ϕ– ϕ = 2πn .
: ;6–
; 3, 4, 5 –
" "
-
-
"
"
2.2.2.
-68-1 ( 2.1)
(
. 2.1
2.2).
.
-68-1 T T
.
.
λ = 0,22 ρ = 1200 / 3, , α = 100 /( 2⋅°C); τ [T(S)] – "Monsanto" " ",
= 50 °C; "
/(
⋅° );
.
. 2.3,
n = 0,2;
"c T
= 80 °C [215]:
(
-68-1 ,%
50,0 50,0 5,00 2,50 75,00 1,00 2,50 3,00 20,00 209,0
-18
-15 " "
8. 9. : Microsoft –
"TablCurve":
τ–
,
-
1).
100
7.
) m0 = 600 000 ⋅ n, = 2100 /( ⋅° ),
(
2.1.
1. 2. 3. 4. 5. 6.
T = 95 °C;
:
,% 23,92 23,90 2,39 1,20 35,88 0,48 1,20 1,44 9,57 100
31,86 24,19 0,54 0,48 26,15 0,62 1,14 1,98 12,74 100 Windows
τ = (–16,17 + 3 131 360/T 2)2,
;T–
, .
2.2.3.
[222 – 224]
-68-1 JB ≤ 0,5 %). (
, , . .
,
(
.
2.1). (2.1) – (2.9) (
2,
. ) :T
.
= 50 °C, T = 95 °C. ω .
, . .
.
(σ , δ Q (2.1) – (2.9) ( (
) N*,
JB, ,
)
, (σ , δ ).
. )
(ω = (0,2…7,85) Q = (0,02…0,1)⋅10–5
∆P, (2.1) – (2.9) (
3
/ ),
. )
–1
.
–
,
,
∆T
N
-
. [225]. (
. 2.3)
" ISO 9000.
"
"Monsanto",
,
Q:
. 2.3. 1– ; 2 – Q = 0,04⋅10–5 3/ ; 3 – Q = 0,06⋅10–5 –5 3 4 – Q = 0,08⋅10 / ; 5 – Q = 0,1⋅10–5 3/ –
,
(σ , δ
.
3
/ ;
(σ , δ )
)
.
-
-250. 269-66. . 2.3 [225, 226]
,
Q
(2, 3, 4, 5)
,
(
1), JB ≤ 0,5
. ( %) 80
/
2
,δ
. = 300 %) 12 %.
. 2.3) 2 %.
(
1)
(
5,
(σ , δ )
(
N σ ,δ ,m ϕ = 17°; h = 0,003 ; D = 0,032 ; L = 0,325 ; ω = 0,2…1,88 ∆P = 5…20 : ––– – ; – , σ ,δ .,σ,δ – , JB – ;τ –
. 2.4)
(σ = -
. 2.4.
Q: –1
; ; ; 14
%.
, .
(2.1 – 2.9)
-
3.
3.1. [222]
-
, . N,
JB
Q, ,
2.
° ); = 2300
⋅°
: ρ = 1200
-68 /(
),
)
(m0 = 100
)
(m0 = 600
⋅
⋅
n
; n = 0,2; T n
=T
.
; n = 0,2; T
.
/ ; λ = 0,22
/(
= 348 ; T = 348 );
.
∆P = 10
= 323 ; T = 348 );
.
. , ϕ
, . 3.1 N,
ϕ
JB . 3.1, h
ϕ
⋅
-
3
Q.
2(
.
. ,
"Linyur") h
(15…20°)
-
N, ,
,
,
-
.
h
N(
1 – 3),
h
,
,
, , ,
,
-
.
)
) 3.1.
–
N ( ), JB (%) ); 0,032 ; ω = 5,2 c–1 (50 / L = 0,32 ; e = 0,0032 ; δ = 0,001 : ; –
Q(
3
/ )
D=
ϕ(
Q . 3.1).
,
h, Q,
h, ϕ
,
, t
, ,
. Q,
, ,
,
ϕ
. . 3.2 JB
-
D
N,
-
ϕ
Q. . 3.2 D
N.
D
N( , ,
h -
,
1, 2, 3),
,
, ,
, .
ϕ(
Q . 3.2).
D,
,
D, , ,
ϕ
,
. 3.3 JB . 3.3,
N.
-
ω
ω
,
1, 2, 3), ,
(
) .
ω, 4, 5, 6),
Q(
4, 5, 6), . N,
ω
ϕ
Q.
N( ,
Q(
Q(
ϕ.
. 3.3)
,
3.1
ω,
3.2,
,
.
)
) 0,01 ; ω = 5,2 c (50 –
. 3.2.
N(
–1
/
JB (%) L = 0,32 ; e = 0,0032 ; δ = 0,001 :
), );
ϕ
JB . 3.4, N
H=
L ϕ,
L
L
N( ,
.
/ )
Q.
,
N.
3
; –
ϕ
. 3.4. N,
Q(
(
1, 2, 3), )
)
) N ( ), JB (%) 0,01 ; D = 0,032 ; L = 0,32 ; e = 0,0032 ; δ = 0,001 : ; –
. 3.3.
–
ϕ.
Q , Q(
. 3.4,
Q(
3
/ )
H=
ϕ,
L, ,
-
4, 5, 6).
)
) . 3.4. ω = 5,2 c–1 –
N ( ), JB (%) 0,01 ; D = 0,032 ; (50 / ); e = 0,0032 ; δ = 0,001 : ; –
Q(
3
/ )
H=
ω,
ϕ ( . 3.1 – 3.4, ω, ∆T ϕ δ JB
JB L, h,
D,
. 3.5 N, . 3.5
N.
.
ϕ
,
N
-
JB,
ϕ ϕ
δ(
,
D, ,
L, .
, N N,
,
h, 7 – 9).
δ
Q.
,
, δ, . .
1, 2, 3),
-
.
)
) . 3.5. JB (%)
ω = 5,2 c–1 (50
–
/ ; –
N ( ), H = 0,01 ; D = 0,032 ; Q ( 3/ ) ); L = 0,32 ; e = 0,0032 :
δ ϕ,
ϕ,
,
. 3.6. JB ϕ. 1, 2, 3), .
δ
Q, ,
( ϕ
Q(
). 4, 5, 6,).
. 3.5,
Q
e
-
N,
Q. . 3.6, ,
N
e, e,
δ, . .
, ,
,
N(
-
)
) . 3.6. JB (%)
ω = 5,2 c–1 (50
–
/ ; –
N ( ), H = 0,01 ; D = 0,032 ; Q ( 3/ ) ); L = 0,32 ; δ = 0,001 : ϕ,
Q
e(
e δ(
ϕ,
. JB . 3.5, 3.6, ∆T
7 – 9).
. 3.6),
-
,
,
ϕ,
JB,
. 3.2. N,
Q(
(ϕ, h, D, L, δ, e)
(ω) ϕ;
JB
. 3.1 – 3.6),
, h;
D;
. (N, JB, Q), . ., ω;
-
: L.
.
4.
4.1.
, – ;
,
:
,
;
F;
-
F; .
,
x –
.
y –
;F–
;
x , y ; R( x , y ) –
,
x,
.
y,
F
.
.
∆P, y3
L; x4 – T
.
, y2 – Q. , (
ϕ; x2 – ; y1 –
ω,
: x1 –
. D
h; x3
y4 –
,
y = (y1, y2),
-
(
: -
. ,
)
-
N
x = (x1, x2, x3, x4, x5) )
x5 –
[222, 226 – 234]:
[F = N(ϕ, h, D, ω, L)]→ min,
(4.1)
: –
R1 = J (t ) = –
(
,
)
i ∂t ∂t ∫ τ[T (t )] = ∑i ∫ τ[T (t )] ≤ ε ; t 0
t*
i −1
(4.3)
= Q(ϕ, h, D, ω, L);
(4.4)
(ϕ, h, D, ω, L) = T ;
(4.5)
Q – T
ϕ*, Dkh*, D*, ω*, DkL* (ω) , , (
,
ϕ*, Dkh*, D*, ω*, DkL* – ; kh*, kL*, kh*, kL*, kh, kL – (h, L), ; ε, Q , T , ).
.
D∗ ≤ D ≤ D ∗ ; ∗ ϕ∗ ≤ ϕ ≤ ϕ ; ∗ Dk h∗ ≤ k h D ≤ Dk h ; ω ≤ ω ≤ ω∗ ; ∗ Dk ∗ ≤ k L D ≤ Dk L∗ ; L
–68-1 . 2.3,
. 2); =
(4.6)
(ϕ, h, D, L) , –
, ; [σ] –
4.2.
(
: τ[T(t)] –
(4.2)
R2(ϕ, h, D, ω, L) ≤ [σ];
–
–
t
,
-
= 2100
/(
⋅°
); ρ = 1200
/ 3, λ = 0,22
T (
.
/( ° ),
⋅
= 323 , m0 = 600
.
T
=T
.
(4.1) – (4.6)
(ω, N) ∆T;
; .
,
;
n
, n = 0,2;
, (ϕ, h, D, L)
-
⋅
, n = 0,2.
Q
; kL* = 5; kL* = 10; ∆P = 25
= 353 , m0 = 100
n
. ),
–1
.
∆P -
: D = (0,03…0,09) ; ϕ = (15…22)°; kh* = 0,05; kh* = 0,15; ω = (1,25…9,4) ; δ = 0,001 ; = 0,1D; D0 = 0,05 ; ϕ0 = 17°; h0 = 0,1D ; ω0 = 3,14 –1; L0 = 7D . . 4.1 4.2, Q , N , ω. Q N, ; δ. ϕ°, h,
D, ω,
–1
L,
N,
∆P = 20 1 – ϕ; 2 – h; 3 – D; 4 – ω; 5 – L; 6 – N (ϕ, h, D, L)
. 4.1. Q ϕ°, h,
. 4.2.
D, ω,
–1
L,
(ω, N) , T = 80 ° :
∆Т, °
N,
(ϕ, h, D, L) Q ∆P = 20 , = 50 °C, T = 80 °C, α = 100 /( 2 ⋅ °C): T 1 – ϕ; 2 – h; 3 – D; 4 – ω; 5 – L; 7 – N; 8 – ∆T (ω, N)
ϕ°, h,
D, ω,
–1
L,
N,
. 4.3. (ω, N) Q = 6⋅10–5 1 – ϕ; 2 – h; 3 – D; 4 – ω; 5 – L; 6 – N
(ϕ, h, D, L) ∆P 3 / , T = 80 ° :
-
ϕ°, h,
D, ω,
–1
L,
N,
(ϕ, h, D, L) ∆P T . = 50 °C, T = 80 °C, α = 100 /( 2 ⋅ °C): 1 – ϕ; 2 – h; 3 – D; 4 – ω; 5 – L; 7 – N
. 4.4. (ω, N)
ϕ°, h,
D, ω,
–1
L,
Q = 6⋅10–5
3
/ ,
N,
(ϕ, h, D, L) (ω, N) ∆T , T . = 50 °C, T = 80 °C, Q = 6 ⋅10–5 3/ , ∆P = 20 α = 100 /( 2⋅ °C): 1 – ϕ; 2 – h; 3 – D; 4 – ω; 5 – L; 7 – N
. 4.5.
ϕ°, h,
D, ω,
–1
L,
N,
α
(ϕ, h, D, L) (ω, N) α , ∆T = 30 °C, T . = 50 °C, Q = 6⋅10–5 3/ , ∆P = 20 T = 50 °C, α = 100 /( 2⋅°C): 1 – ϕ; 2 – h; 3 – D; 4 – ω; 5 – L; 7 – N
. 4.6.
ϕ°, h,
D, ω,
–1
L,
N,
(ϕ, h, D, L) Q
. 4.7. (ω, N) 1 – ϕ; 2 – h; 3 – D; 4 – ω; 5 – L; 6, 7, 7' – N –
: ,
,
, J 1(t) ≈ 0,003, J 2(t) ≈ 0,006. ,
,
, . . -
, . ω.
. 4.1 – 4.7,
Q,
Q
N, ;
N
-
δ.
;
∆T,
. 4.1 – 4.4 . 4.5 , ∆T, .
,
ϕ(Q), h(Q), D(Q), ω(Q), N(Q) L
. , ,
ω
,
h ω.
. ∆T
h
-
Q, N
-
,
ω
.
. 4.6
α
D ϕ,
. D
∆T
, h,
,
ϕ
L. D. :
. -
L, Q, α),
(
h
. :
(2.3); (
.
. . 2.1 ,
1,5…3,0 (∆T = 30 )
m0 = (6…1)⋅105 ⋅ n, . (ϕ, h, D, L) ,
, , (
. 4.7).
(2.5) . 2).
(2.7),
,
-
,
(ω, N)
-
.
ω.
. 4.1, 4.2, 4.7,
Q
N
Q
N,
δ.
: ;
-
; .
, . , (ω, N) ∆T
4( ∆P, ,σ
,
. 4.1 – 4.7),
(ϕ, h, D, L) Q,
, ≤ [σ] (
EJ ≤ [EJ]
y ≤ [y])
,
-
.
4.3. (
. . 4.1)
,
. 2.2.1.
. 4.3.1.
-68 JB ≤ 0,5 %).
, , . .
,
(
= 0,003 , D = 0,032 , L = 0,325 , e = 0,0035, δ = 0,001 ) (2.1 – 2.9) ( , . . ) .
(ω = 6,28 , . . :T
ω.
h
–1
,
.
-
= 323 , T = 368 . :
h, ω
)N (0,2…6,28)
, ϕ = 17°, h
–1
∆T,
0,0005 ) (2.1 – 2.9) (
(
ϕ = 17°, D = 0,032 , L = 0,325 , e = 0,0035, δ = 0,001 , Q = (0,02…0,08)⋅10–5 3/ ), (JB ≤ 0,5), (σ ≤ 320 (h0 = 0,003 , ω0 = 0,2 –1) , . . )
-
Q
. ∆P, ,
(ω = y≤ -
N. ; ω = (0,2…7,85)
h = (0,002…0,006)
–1
.
. 4.2. (h* = 0,0025, 0,0035, 0,0045 )
(
.
. 4.8,
. 4.1) ISO 9000).
, Windows
" ( . 4.8, "TablCurve":
Microsoft –
. "Monsanto" (
" 1)
τ = (–16,17+3 ⋅ 106/T 2)2,
τ–
,
;T–
, .
4.1. τ,
-68-1 τ,
-
T,
50
45
370
27
25
380
20
18
390
. 4.8.
:
1– Q⋅10 , 3/
5
;2–
4.2.
∆P,
–
T
JB,
,
.
h*,
%
0,2 0,3 0,4 0,5 0,6 0,7 0,8
-
5 5 5 10 10 15 15
100 100 100 90 90 80 80
0,5 0,5 0,5 0,5 0,5 0,5 0,5
0,0025 0,0029 0,0032 0,0035 0,0038 0,0041 0,0045
(σ , δ
, .
-250.
ω*,
N*,
1,88 3,12 3,75 5,02 5,65 6,91 7,52
0,15 0,25 0,41 0,52 0,61 0,82 0,94
–1
.
-68-1 (σ , δ )
)
-
269-66. δ
.
= 300 %)
(σ , δ )
(
. 4.9)
(σ = 80
2
,
10 %. ,
(
/
) (JB < 0,5 %)
(σ
≤ 320
. 4.10), y ≤ 0,0005 ) . (
,
-
σ ,δ ;σ ,δ .,σ ,δ –
. 4.9 ; –
––– –
N Q:
;τ –
JB –
h, ω ;––– –
. 4.10. –
, ;
,
N Q:
(
.
. 4.10)
-
(14 %), (
) .
4.3.2.
(0,2…12,85)
–1
∆T,
,
. 4.3.1
" ( . 2.2), . 2.2.1. : T . = 50 °C, T = 95 °C. (ϕ = 17°, D = 0,06 , L = 0,6 , e = 0,0065, δ = 0,001 ), Q = (1…6)⋅10–5 3/ ), ∆P, (JB ≤ 0,5), (σ ≤ 300 (h0 = 0,003 , ω0 = 0,5 –1) (2.1 – 2.9) ( , . ) "
0,0005 )
-
,
(ω = y≤
N.
h = (0,003…0,008)
; ω = (0,2….12,85)
–1
.
. 4.3.
(h*
= 0,0035, 0,0060, 0,0080 )
,
. 4.3.1.
, (
-
) JB < 0,5 % [222].
( (
%),
. 4.11),
. 4.11)
(14 (
).
Q⋅ 10 , 3/ –5
1 2 3 4 5 6
∆P,
4.3. °
10 10 10 15 15 20
∆T,
100 100 100 90 90 80
. 4.11. –
JB, %
0,5 0,5 0,5 0,5 0,5 0,5
h, ω ;––– –
H*,
ω*,
N*,
8,91 9,41 10,4 11,5 12,5 12,7
1,05 1,84 2,76 4,34 5,46 7,52
–1
0,0035 0,0050 0,0060 0,0065 0,0078 0,0080
N Q:
5.
5.1. , ( . 2), ,
. .
. . [74]: 1)
,
(
. .
,
-
[94]
) N = N1 + N2 + N3,
(5.1)
N1 = (B/h)(4Vx2 + Vz2)m0(V/h)n – 1z Fz; N2 = (Vz/2)Bh∆P;
1 Fz = z 2)
∫ exp RT ( z) ∂z ; N
z
E
3
z = L/sinϕ; V = ωD/2.
0
Q1 = (Vz/2)(B/h)Fg; Q2 = Bh F ∆P/[12(V/h) : 3
3) )
= V(V/δ)nm0exp[E/(RT )]ecos(ϕ)z ; Vz = Vcosϕ;
Q = Q1 – Q2,
(5.2)
n–1
m0Fzz ].
T(z) = T + Gexp[E/(RT)] – (Gexp[E/(RT)] – T
2
G = m0h /(2Kλ)(V/h)
; A = 2KaB/(Qh); a = λ/(ρc); K = αh/λ; V = Q/Bh.
.
+ T )exp(–Az), (5.3)
n+1
T : T = T + Gexp(E/RT )(1 + (exp(–Az ) – 1)/(Az )) + + (T – T . )(exp(–Az ) – 1)/(Az ); )
(5.4)
[231] T(z) = T T
.
=T
.
.
+ GBh/(ρcQ)exp(E/RT )z.
(5.5)
T : + GBh/(ρcQ)exp(E/RT)z /2;
(5.6)
) T 4)
.
=T
.
η = m0 γ& n −1 exp
5) [125, 126]
,
,
JB(t ) =
∫ τ[T (t )] –
t*
∂t
; τ[T(t)] – p
(5.7)
E . RT
(5.8) JB (
)
i ∂t ∂t = ∫ τ[T (t )] ∑i ∫ τ[T (t )] = 1 , t 0
t*
,
.
t
(5.9)
i −1
p
p
( p
-
0
" T(t).
p
"
p ); t* – p
p
"
p
" p
p
-
(
)
,
,
,
.
, –"
-
",
" (
". . 5.1)
, . . . , . .
,
–
. .
.
,
,
"
"
.
-
(
),
"
",
,
.
( )
"
",
-
[235].
ln
l
l
1
D
D
D
D
D1
Dn
D2
-
l
2
l
. 5.1.
:
1, 2 –
;3–(
); 4 – ;5–
γ,
. -
, [211, 222, 236 – 240].
γ& –
γ& =
τ–
W = (t – e)cosφ – (n = 0,2); , ;h–
γ
[241 – 243]:
= γ& τ , 1 ω + 1 n
,
–1
[111],
;
h
, .
WhL ; τ = Q sin ϕ
, ;Q– , –1; φ – , .
–
,
3
/ ;n– , ;L–
γ = ∑γ i ,
:
n
γ
i
= γ& i τ i ; τ
i
i =1
Fl = i i ; γi – Qi i-
,
6) [236 – 243]:
; γ i , γ& i , τ
i
–
,
,
; Fi , li –
i-
,
,
.
,
γ = γ + γ = γ& τ + (5.10)
∑ γ& i τ i . n
(5.10)
i =1
,
(
)
. , . (
. 5.1). ,
D
∂l
, l,
V = Q/(πD2/4), QL l
ql = ρ V T.
. 5.2. V [94]:
(5.11) (5.12)
:
∂ql /∂l= ρ V (∂T/∂l).
(5.13)
q = τ γ& = η γ& 2 ,
γ& = 2V/D,
,
(5.14) :
~ 1 T = ∫ T (l )∂l . l0 l
,
(5.15)
α
,
-
q = α(T – T ).
(5.16)
α = 2Kλ/D. :
qlBH + q BH∂l = [ql + (∂ql/∂l) ∂l]BH + q B∂l, . l
q
l
(5.17)
q
l+
q dl ld l
dl
q
V
qk
D
. 5.2.
. 5.3. ( 1(
G1 =
m1D12 8V1 4kλ1 D1
n +1
; A1 = 4k1
a1 V1 D12
. 5.3)
; a1 =
) E E T (l ) = T1 + G1 exp ~ − (G1 exp ~ − Tnb + T1) exp(− A1l ) . RT1 RT1
λ1 . ρ1c1
E e − A1l1 − 1 − A1l1 ~ + (− Tnb + T1 ) e T 1 = T1 + G1 exp ~ 1 + , A1l1 A1l1 RT1
(5.18)
(5.19)
[43, 211]
γ& 1 = 2(
8V1 . D1
. 5.3)
-
. ,
,
я( ,
. 5.3)
V2 = n –
(n = 3):
-
4Q
n πD22
,
E T (l ) = T2 + G2 exp ~ RT 2
m D 2 8V G2 = 2 2 2 4kλ 2 D2
n +1
E ~ T 2 = T2 + G 2 exp ~ RT 2 ; A2 = 4k 2
a2 V2 D22
λ2 . ρ 2 c2
; a2 =
− T + T ) exp( − A l ) . (5.20) 2 2 1b
− (G exp E 2 ~ RT 2
−A l −A l 1 + e 2 2 − 1 + (− T + T ) e 2 2 , (5.21) 1 2 b A2 l 2 A2 l 2
[43, 211]
γ& 2 = (
. 5.3)
,
-
D = D = f (l ) , D (l ) = D
.
−
l (D l
−D
.
.
D
.
+D 2
):
.
(5.22)
− G exp E ~ RT
E T (l ) = T + G exp ~ RT
G =
8V2 . D2
m D 2 n +1 (γ& ) ; A = 4k a 2 ; 4kλ V D (l ) a =
[43, 211]
−T +T 2b
E ~ T = T + G exp ~ RT
exp(− A l ) . (5.23) −A l e− A l −1 1+ + (−T2b + T ) e , A l Al
λ 4Q . ; V = ρ c πD 2 (l ) γ& = (
256Q
π( D + d ) 3
.
. 5.3)
:
− T b + T exp(− A l ). (5.25)
E E T (l ) = T + G exp ~ − G exp ~ RT RT
Gp =
mp Dp2 4kλ p
(γ& )n+1 ;
[43, 211]
(5.24)
~ E T p = Tp + Gp exp ~ RT p Ap = 4k p γ& =
ap Vp Dp2 8Vp Dp (
; ap =
. . 5.4).
(
−A l e p p − 1 1 + + −T Ap l p
λp
ρ p cp
; Vp =
4Q
πDp2
.
b + Tp
) eA l
− Ap lp p p
;
(5.26)
l
q
q
l+
q dl ld l
dl
q
V
qk
D
D
. 5.4. ,
:
V ql
(
π[ D − D 2 (l )]
D (l) − D
D (l ) − D 2
(5.27)
(5.28) -
= α(T − T ) ,
q ; H=
.
α
), :
2
4Q
2
ql = ρ c V T .
,
α = kλ
=
(5.29)
.
(
. 5.4)
ql π( D (l ) − D ) π( D (l ) − D ) dl = +q 4 4 2
2
2
:
2
dq π( D 2 (l ) − D 2 ) + q πD dl. = q l + l dz ⋅ 4 dz ρcV
2 D (l )kλ dT E (T − T ) . = m γ& n +1 exp ~ − dl ( D (l ) + D ) RT l
(
. 5.1)
T (l ) = T
+G
− G
T =T ~
G
=
m ( D (l ) + D ) 4kλ D (l )
( γ& ) n +1 ; A
= 4k
a D (l )
V ( D (l ) + D ) =
λ
ρ l
D +D 4
; Rb =
D +D 4
; δ1 =
D −D
;
.
2
22,32Q 1 ; π( R0 + Rb ) (δ1 + δ 2 ) 2
; δ2 = (
D −D 2 . 5.1)
.
−
− T2 b + T
exp( − A l ).
−A l − 1 e ⋅ + 1 + (− T2b + T A l
[43, 220]
γ& =
E exp ~ RT
E exp ~ RT
E exp ~ RT
+G
a
R0 =
(5.30)
)e
−A
A l
(5.31)
l
, (5.32)
T (l ) = T
G
m (D + D )
=
4kλ D
= 4k
γ& n+1 ; A
− (G
E exp ~ RT
+G
~ E T = T + G exp ~ RT a D V (D + D ) a
=
λ
ρ l
−T
E exp ~ RT
+ T ) exp( − A l ) . (5.33)
(
−A l − 1 e + −T +T 1 + A l
) eA
−A l
l
, (5.34)
;
.
[43, 211]
γ& =
R =
D 2
; R =
D 2
.
;σ
7)
5,58Q 1 , π( R + R ) ( R − R ) 2
≤ [σ],
( EJ ≤ [EJ], y ≤ [y],
, .
)
(5.1 – 5.10)
-
.
5.2.
5.2.1.
(5.1) – (5.10)
-
. . ( ϕ = 17°,
D = 0,032 , h = (0,002…0,005) , – δ = 0,001 . ,
,
. 5.2) [244, 245], L/D = 10,
= 0,0035 , ω = (0 …7,85) ,
, ).
(
)(
–1
.
-
. , . (100 ± 1 º ),
.
,
( – 1050…1100 / 3.
),
,
.
( .
. 5.3),
.
–
–
N=N
− N xx ; N
.
= I U ; N xx = I xxU ,
-
:
:
. 5.5.
,
N– ;N –
, ,
;N – ;I –
, ;I –
, ;U–
, .
1
2
3
60°
60°
. 5.6.
1–
;2– 5–
9– 12 –
:
;3– ;6– ; 10 – ; 13 –
;7–
PE –
;A–
;4– ;8– ; 11 – ; TE – ;V–
; ; ; ;
. 5.7 . ,
, ,
,
-
.
-
,
.
. 5.7.
:
1– 9–
4– ; 12 –
; 10 –
; 2; 11 – ;6– ; 14 –
;5– ; 13 –
;3–
;
;8–
; ; 15 –
; 16 –
-
5.2.2. -68-1 (
-68-1
:
T = 85 °C;
T (
" 0,22 , ",
"c /( ⋅° );
T
= 80 °C (
-
) m0 = 600 000 [215],
.
= 50 °C;
⋅ n, n = 0,2; = 2100 /( ⋅° ),
( .
. 2.3,
-
. 5.5, 5.6). T = 100 °C; T
.
ρ = 1200 / 3, λ= α = 100 /( 2⋅°C); τ[T(S)] – "Monsanto" " -
1). Windows
Microsoft –
"TablCurve":
τ–
,(
τ = (–16,17 + 3131360/T 2)2,
); T –
, .
5.1.
-
-68-1 100 -
1. 2. 3. 4.
-18
5. 6.
-15 7. " "
8. 9. :
-
,%
,%
50,0 50,0 5,00 2,50
23,92 23,90 2,39 1,20
31,86 24,19 0,54 0,48
75,00 1,00 2,50
35,88 0,48 1,20
26,15 0,62 1,14
3,00 20,00 209,0
1,44 9,57 100
1,98 12,74 100
5.2.3.
,
"
[243 – 246]
-
", . .
(
), :
" .
-
.
-68-1,
" ,
-
20 .
(
)
. = (0,4; 1,04; 3,12; 5,2; 5,76; 6,24; 7,28)
= (8,4; 10,4; 16,4; 18,4)
);
.,
-
.
30 2 –1
d
.
° –
:T
,°
.
– (
);
.
,° –
-
(
. ; I,
–
: P, .– ; Q, / –
, (
/(2
)
, ,
-
. 5.8).
-
/ ). ,
(7,2
)
"Adop PhotoShop 5.0" ( ) (
( )
,
, %,
.
) . 5.8. : –
5
;
–
10
)
. 5.8. 5.2.4.
,
γ
Q
[247]. .
,
-
(
)(
γ
. 5.2,
γ,
. 5.9) [248], . .
.
,
,
[125, 126]. ,
, . 5.9.
(5.1 – 5.10). γ&
,
10 %) Q,
7
. 5.9. 2
Q=7 , ,
/
9
/ (
( 20
.
–1
15
. 5.10),
/ , N = 1060
–1
,
N,
Q=9
/ , N = 1180
(
1060
. 5.10). (20 ° )
(
. 5.2.
T
103
γ 50
100
40
40
97
30
30
94
20
20
91
10
10
88
0
0
.
.,°
. .,
δ, % 50 −1
1 3 4 2
0
. 5.9.
20 δ
γ&
(2), Т
.
. (4)
40
60
80
(1) .
(3)
1180
γ
.
γ
. .
= -
.
= 100 ° ) (45 %), , .
T
110 100 90 80 70 60
. .,
γ
, °C N ,
.
c
−1
1200 100 1120 80 1040 60 3 40 960 2 880 20 1 800 00
5
10
. 5.10. γ& . (1),
Q
(3)
.
(
. 5.9,
2) γ
. .
/
N (2) Т
γ
Q,
.
, = 30…90
30
= 90…95,
95, -
. , ,
, ,
,
,
" γ
, ,
"
"
-
, " .
. -
.
. . -68-1 JB ≤ 0,5 %).
, ,
(
, . . (5.1) –
(5.10) (
3,
. ) :T
. .
= 50 °C, T = 85 °C. ω .
, . .
.
( ) N*,
(σ , δ Q (5.1) – (5.10) (
.
–
, (σ , δ ). (ω = (0,2…7,85)
)
-
,
3,
Q = (0,02…0,1)⋅10–5
. ), ∆P, (5.1) – (5.10) ( .
3
/ ),
N,
(
-
JB,
JB
. 5.11)
"
-
"
–1
,
-
. ), [240]
"Monsanto",
∆T
-
[224].
-
,
-
ISO 9000.
: 1–
. 5.11. –5
4 – Q = 0,08⋅10–5
3
0,06⋅10 / ; 3 / ; 5 – Q = 0,1⋅10–5
3
/ –
; 2 – Q = 0,04⋅10–5
3
/ ;3–Q=
(σ , δ
, -250.
.
(σ , δ )
)
.
-
269–66. . 5.11 [220]
,
Q (
(2, 3, 4, 5)
,
-
1), JB ≤ 0,5 %)
. (
. 5.11)
(
1)
(
5
2 %. (
. 5.12)
m0 = 600 000 ⋅ n, n = 0,2; = 2100 /( ⋅° ),
T
.
= 50 °C;
T = 85 °C;
λ = 0,22 ρ = 1200 / 3, α = 100 /( 2⋅°C); τ[T(S)] – , "Monsanto" " ", . . 5.11,
(
,°
JB, % Т
. 5.12. (■)
γ&
.
T
.
) -
1).
δ (□)
,
γ&
.
(●),
(
(▲)
),
(∆) n
JB (♦) d
( /
( [224]):
δ, %
T
n = 50…70 ,
-
T = 105 °C; T = 75 °C ( /( ⋅° );
:
. 5.12,
.
(□)
.
= 0,01
(■))
n = 10…50
/
,
-
,
,
. ,
80…95 % .
JB ( 4
. 5.12, 1 %)
20
n 50 70 / 99 103 °C 18 %.
n
10
50
96 18,5 20 %. (1 %)
JB ,
/
,
99 °C
-
(
%)
, . δ, % 24
JB, % 15 2
16
10
8
5 1
0
0 90
100
. 5.13. d
.
T = 0,0105
110
T
, °C δ (2),
l = 0,008
JB (1)
4
(
. 5.12)
,
(5.18) – (5.34) 2 %.
(
. 5.13)
,
,
-
JB (σ , δ )
= 300 %)
(
N σ ,δ Q ϕ = 17 ; h = 0,003 ; D = 0,032 ; L = 0,325 ; ω = 0,2…1,88 ∆P = 5…20 : ––– – ; – ;σ ,δ .,σ ,δ .–
. 5.14)
. (σ = 80 / 11 %.
,δ
2
.
. 5.14.
, τ –
; JB – ; –
–1
; ,
;
12 %. , .
(5.1 – 5.10)
-
6. ,
6.1.
, . N, JB
-
,
-68-1 ⋅ n; n = 0,2; T
4.
⋅ ; n = 0,2; T . = T . (m0 = 100 = = 323 ; T = 358 ; ∆P = 20 ). n
.
Q,
, : ρ = 1200 = 358 ; T = 358 )
/ 3; λ = 0,22
/( ⋅° );
= 2300
.
/( ⋅° ); (m0 = 600 -
, ,
5(
. 6.1
.
ϕ
. ,
h
1 "Linyur"). h
JB ϕ
Q, . 6.1,
1
N,
. ϕ
(15…20°) N, ,
–
650
–
630
–
600
-
,
– 3⋅10– 3 /
5
–
600
–
500
–
400
– 1 5 10–5
. 6.1.
(20 –
N (1 – 3), Q (4 – 6), JB (7 – 9) γ (10 – 12) D = 0,032 ; ω = 2,1 c–1 –1 ); L = 0,32 ; e = 0,0032 ; δ = 0,001 : ; –
,
.
h
N(
1 – 3),
h
,
, , ,
,
ϕ(
.
Q . 6.1).
,
h, h,
Q,
ϕ
h . Q, ,
,
,
, t ϕ,
JB
ϕ.
, γ& ,
h, (
, -
.
h,
, ,
. 6.1).
,
h, ,
,
,
ϕ
Q .
. 6.2 N,
Q,
JB
. 6.2, D
ϕ
D
ϕ
-
.
D
N. 1, 2, 3), ,
N( ,
,
-
, ,
,
,
.
Q(
ϕ(
4, 5, 6),
Q . 6.2).
D,
,
D, ,
, ,
-
. ϕ
JB (
D, D
. 6.2).
,
Q, ,
.
– 500
– 1000
– 1500
1 – 10 000
–
2 8000
–
3 6000
4 – 9⋅10–6 3
) . 6.2.
–
(
. 6.2).
N (1 – 3), Q (4 – 6), JB (7 – 9) ); γ (10 – 12) H = 0,004 ; ω = 3,14 c–1 (30 / L = 0,32 ; e = 0,0032 ; δ = 0,001 : ; –
ϕ,
ϕ,
, Q
ϕ
. 6.3. N, ω
Q, . 6.3,
ϕ
D ,
JB N.
. ,
ω
. ω
-
N(
1, 2, 3), ,
)
(
-
,
.
ω, (
ϕ.
Q(
ω,
. 6.3)
,
Q
4, 5, 6),
. N (1 – 3), Q (4 – 6), JB (7 – 9) γ (10 – 12) H = 0,006 ; D = 0,032 ; L = 0,32 ; e = 0,0032 ; δ = 0,001 : – ; – . 6.3.
1 – 1500 2 – 1000
–
3 500
4 – 9⋅10–6 3 /
1 – 4000 2 – 3000 3 – 2000 4 – 9⋅10–6 3 /
–
1 200
–
2 150
–
3 100
. 6.4.
– 9⋅10 3 /
D = 0,032 ; ω = 5,2 c–1 –
4
N (1 – 3), Q (4 – 6), JB (7 – 9) γ (10 – 12) H = 0,006 ; (50 / ); e = 0,0032 ; δ = 0,001 : ; –
–6
1 – 4000 2 – 3000 3 – 2000 4 – 9⋅10–6 3 /
ω,
JB ω
6.3). Q, ,
ϕ(
. ,
.
ϕ,
ϕ,
, .
ϕ
. 6.4. JB ϕ
Q, . 6.4, , L
N
ϕ,
N,
L 1, 2, 3), ) ϕ.
, ,
. ϕ,
L, ,
4, 5, 6). JB L L, L, ϕ
. N,
.
,
δ Q,
JB ϕ
, ),
N(
).
δ, . .
. 6.3).
.
,
. 6.5
3),
ϕ(
ϕ(
.
, N N(
-
L,
,
. 6.5
-
N.
(
Q
6.4). ,
,
L
N(
. 6.4,
. 6.3). Q
.
,
Q(
ω(
,
.
ϕ,
δ,
ϕ
, δ(
N
,
–
1 150
–
2 100
, 1, 2, -
.
3 – 50 4 – 3⋅10–6 3 / 5
1 – 1300 2 – 1100
–
3 900
4 – 3⋅10–6 3 /
N (1 – 3), Q (4 – 6), JB (7 – 9) γ (10 – 12) H = 0,004 ; D = 0,032 ; –1 ); L = 0,32 ; e = 0,0032 : ω = 3,76 c–1 (35 ; –
. 6.5.
– δ ,
ϕ, JB
, (
.
. 6.5, ), δ
ϕ,
Q, ( Q(
δ,
. 6.5,
). 4, 5, 6).
Q ϕ(
(85 °C)
. 6.5, ) -
.
ϕ,
ϕ,
δ(
. 6.5).
,
,
. . 6.6 Q,
ϕ .
JB
e
N,
-
1 – 2000 2 – 1500 3 – 1000 4 – 2⋅10–6 3
1 – 7000 2 – 6000 3 – 5000 4 – 2⋅10–6 3 /
N (1 – 3), Q (4 – 6), JB (7 – 9) γ (10 – 12) H = 0,004 ; D = 0,032 ; ); L = 0,32 ; δ = 0,001 : ω = 3,14 c–1 (30 / ; – N e, , . 6.6.
– ϕ. 1, 2, 3),
. 6.6, , δ, . .
( -
,
, ϕ,
. Q
e(
. 3.6),
-
, ϕ,
. (
6.6).
∆T
. 6.6,
JB 7 – 9).
ϕ,
, ϕ,
,
JB, ϕ, ,
.
(
.
. 6.2. N, JB
(
(ϕ, h, D, L, δ, e)
(ω) (N, Q, JB, ), . .,
, h;
Q,
-
. 6.1 – 6.6),
D;
ω
. : L.
-
7.
7.1.
,
,
-
:
( γ
,
),
,
, [126].
:
, )
-
[243].
-
(
[F = N(h, D, ω, L)]→ min,
:
(7.1)
: –
(
)
∫
t∗
R1 = JB(t ) =
0
–
(
–
)
(
∂t = τ[T (t )]
)
Dkh*, D*, ω*, DkL* Dkh*, D*, ω*, DkL* – , ; kh*, kL*, kh*, kL*, kh, kL – (h, L), ; ε, γ
(7.3)
= Q(h, D, ω, L);
(7.5)
(h, D, ω, L) = T ;
(7.6)
.
D∗ ≤ D ≤ D ∗ ; ∗ Dk h∗ ≤ k h ≤ Dk h ; ω∗ ≤ ω ≤ ω∗ ; ∗ Dk L∗ ≤ k L ≤ Dk L ,
(7.7)
(h, D, L) ,
(ω)
,
,Q ,T .–
,
,
, ). : ϕ = 17o; ε = 0,02; γ
(
0,05; kh* = 0,15; ω = (1,2…9,4) –1; kL* = 5; kL* = 10; ∆P = 20 0,05 ; h0 = 0,1D ; ω0 = 3,14 –1; L0 = 7D .
;
(7.4)
Q
–
(7.2)
R3(h, D, ω, L) ≤ [σ];
– T
∂t
i −1
R2(h, D, ω, L) = γ
–
, ; [σ] –
∑ ∫ τ[T (t )] ≤ ε ; i t ti
; δ = 0,0005 ; α = 100
= 3500, T /(
2
⋅ °C); T
-
= 90 ° ; D = 0,03…0,09 ; kh* = = 50 °C, T = 85 °C; = 0,1D; D0 =
7.2.
(7.1) – (7.7) ( . 7.1, 7.2).
, . 7.1.
,
[212],
Q
, .
. 7.2
,
Q
ω
D,
γ
ω,
L,
3500 400 3,0
75
5
2800 320 2,4
60
4
2100 240 1,8
45
3
( –1
D,
. 7.1) –
h,
N,
3,0
1 5 6 4 2
2,4 1,8
3 1400 160 1,2
30
2
1,2 0,6
700
80
0,6
15
1
0
0
0
0
0 0
0 5
10
15
20
25 Q,
/
(3 – ω, 5 – N, 6 – γ)
. 7.1.
(1 – h, 2 – D, 4 – L) Q γ
L,
ω,
–1
D,
h,
N,
60 6,0
400
3,0
320
2,4
48 4,8
240
1,8
36 3,6
3,0
5 2 4 1
2,4 1,8
3 160
1,2
24 2,4
1,2
80
0,6
12 1,2
0,6
0
0
0
0 0
5
10
15
(3 – ω, 5 – N)
(1 – h, 2 – D, 4 – L) Q
. 7.2.
(
D . 7.1
N 6,2 / ) –1 ; L = 0,325 ; ∆P = 20
h, . . 7.2) Q.
; δ = 0,0005 ; α = 100 -32
0,032 ; kh* = 0,05; kh = 0,15; ω = (1,2…9,4) = 0,1D; h0 = 0,1D ; ω0 = 3,14 –1.
/(
(Q = 6,2 , ω,
–1
2
⋅ °C); T
5
5
2920
4
4
.
; L = 0,325 ; ∆P = 20
.
)
(Q =
: ϕ = 17o; D = 0,032 ; ω = 2,2 = 100 °C; T = 85 °C; = 0,1D; h = 0,0035 . ( . 7.3 7.4) = 3500; T = 90 ° ; D = : ϕ = 17o; ε = 0,02; γ
; δ = 0,0005 ; α = 100
N ,
/ )
/(
2
⋅ °C); T
,
.
= 50 °C; T = 85 °C;
13 %
-
.
h,
3650
(N = 0,865
-32 = 50 °C; T
–1
,
γ
-
( γ = 4475),
*
. 7.3 7.4
0 /
25 Q,
20
N,
1,0
6 1
0,8
5 2190
3
3
1460
2
2
0,4
730
1
1
0,2
0
0
0
0,6
3
0 5
6
7
8 Q,
/
(3 – ω, 5 – N, 6 – γ)
(1 – h)
. 7.3. Q
γ
-
ω,
–1
h,
N,
5
5
4
4
1,0
1
0,8 5 0,6
3
3 2
2
1
1
0
0
3
0,4 0,2 0
5
6
7
8
Q, /
(3 – ω, 5 – N)
. 7.4.
(
(1 – h) Q
. 7.3)
Q,
ω
,
h. ,
,(
-
.
-
).
Q ω.
. 7.1 – 7.4, Q
N N, ;
:
-
δ.
; .
-
,
. ,
(ω, N)
7(
∆T
∆P,
. 7.1 – 7.4),
(h, D, L) ,
,σ
≤ [σ] (
-
Q,
EJ ≤ [EJ]
y ≤ [y])
,
, .
7.3. (
. . 7.1)
,
. 7.2.1.
. 7.3.1.
-68 JB ≤ 0,5 %).
, , . .
,
(
(ω = 6,28 = 0,003 , D = 0,032 , L = 0,325 , e = 0,0035, δ = 0,001 ) (7.1 – 7.10) ( . , 3) :T ω.
h )N (0,2…7,85) , 1
)
–1
,
y ≤ 0,0005 )
.
, ϕ = 17 , h
–1
, . . = 323 , T = 358 .
. :
h, ω Q ϕ = 17 , D = 0,032 , L = 0,325 , e = 0,0032, δ = 0,0005 , Q = (2…8)⋅10–7 3/ ), ∆T, (JB ≤ 0,5), (7.1 – 7.7) (
h = (0,002…0,006)
. , N.
3)
; ω = (0,2…7,85)
–1
.
(
.
(ω = ∆P, (σ ≤ 320 (h0 = 0,003 , ω0 = 0,2 – -
7.3.2.
(
(h* = 0,0025; 0,0032; 0,0035 )
. 7.1) .
7.1.
∆P,
Q⋅10–5 3 /
T
JB
,
.
, %
%
0,2 0,3 0,4 0,5 0,6 0,7 0,8
5 5 5 10 10 15 15
100 100 100 90 90 80 80
h*,
0,5 0,5 0,5 0,5 0,5 0,5 0,5
3450 3450 3450 3450 3450 3450 3450
5 5 5 7 7 10 10
0,0025 0,0029 0,0032 0,0035 0,0038 0,0041 0,0045
ω*,
N *,
1,88 3,12 3,75 5,02 5,65 6,91 7,52
0,15 0,25 0,41 0,52 0,61 0,82 0,94
–1
. ( . 7.5, ISO 9000).
. 7.2)
"
-
"
"Monsanto" (
, (σ , δ
, .
-250.
-68-1 (σ , δ )
. )
-
269-66. Windows τ–
δ
.
= 300 %)
( . 7.5, "TablCurve":
Microsoft –
1)
τ = (–16,17 + 3·106/T 2)2,
,
;T–
, .
(σ , δ )
(
. 7.6)
(σ = 80
10 %.
7.2.
-68-1
τ,
τ,
50 27 20
T,
45 25 18
. 7.5. 1–
370 380 390
: ;2–
/
2
,
σ ,δ
. 7.6. ; –
––– –
N ;σ ,δ
;τ –
JB –
;δ– ; –
Q: , σ ,δ . ,
–
,
-
;
, ( 320
,
) y ≤ 0,0005 )
( (JB < 0,5 %) .
( = 3450) (
. 7.5), (σ
. 7.6)
(11 %), (
≤ , -
) .
8.
(
5, 6, 7)
.
1.
, m0; n – τ[T(t)] –
,
: T
.
;
;
xi∗ ≤ xi ≤ xi∗ –
;
∆P; ∆T – Q– [σ] –
,
;
; (
ε–
,
)
-
; .
2.
.
РИ НТ 1. .
2.
.
3.
( . 5) ( . 7, – –
(7.1 – 7.9))
(
(ω, N) (ω, N)
,
(h, D, L) (h)
( (
. )
:
1); 2).
,
, . [211]. -
[σ] = 320
: = 2100 , [y] = 0,0005 . 1.
/( ⋅° ), ρ = 1200
-68-1. / 3, λ = 0,22
/( ° ), T = 358 , m0 = 600
(ω, N)
(ϕ, h, D, L)
(ω, N)
(h)
⋅ n, n = 0,2
T
.
.
.
= 323 , . 7.2,
. 7.2. 2.
h0 = 0,003 ; ω0 = 0,2
–1
; h = (0,002…0,006)
. ; ω = (0,2…7,85)
.
. 8.1.
: –1
.
: a = 0,016 ; l = 0,32 ; [y] = 0,01R1 ; (0,001 ≤ 1 ≤ 0,006) ; ; = 2 ⋅ 105 ; µ = 0,3; ρ = 7,85 ⋅ 103 / 3. 4) [211], , : h = 1* = 0,0025 ; e = 2* = 0,0024 ; R0 = 3* = 0,0078 . *min = 6,56 , 20 % . ( . 1.24, 1.25, 1.26) : = 0,016 ; = 50 ; [σ]1 = 566 ; [σ]2 = 434 ; 0,022 ≤ 1 ≤ 0,028 ; 0,028 ≤ 2 ≤ 0,032 ; 0,032 ≤ 3 ≤ ≤ 0,042 ; 0,006 ≤ 4 ≤ 0,012 . "minMT-LC" ( . , 5) [211] : ; 1* = 21,9 ; ; ; 2* = 28,6 3* = 32,8 4* = 6,6 *min = 0,03 , 20,5 % . ( . 1.27) R1 = 0,016 ; = 50 ; (0,001 ≤ 2 ≤ 0,004) ; (0,001 ≤ 3 ≤ 0,01) ; "minMSCRE" ( . ,
1.
, ,
2. 3.
. . (∆T, ∆P, ω).
,
4. N( JB
Q,
),
,
.
5. . 6.
N( Q, T
.
JB,
) (
)
.
7.
.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62.
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.:
-
63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76.
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.
.
-
:
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:
,
: .
. 103.
: .
104. , 1978. 105.
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, 1978. . 43 – 46. . . , 1978. . . //
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:
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206. 207.
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A.M.
. .: . . 05.04.09. ., 1999. 32 .
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: . .… . 208. . ., . ., . ., . . . .: , 1984. 152 . 209. . . , : .… . . 05.17.08. , 1984. 377 . 210. . . , : .… . . 05.02.13. , 2001. . 390. 211. : / . . , . . , . . , . . , . . . .: " -1", 2004. 248 . 212. . . .: , 1975. 480 . 213. // . . . ./ . . ; . . .: , 1983. 214. Rajesh J., Jayaraman V.K., Kulkarn B.D. Taboo search algorithm for continuous function optimization. Chem. Eng. Department, National Chemical Laboratory, Pune. India. Che. Eng.: Res and Des. A: Transactions of the Institution of Chemical Engineers. 2000. 78. № 6. 215. . . : .… . . . ., 1972. 216. . ., . ., . . // : . : . . . - , 1999. . 3. C. 72 – 74. 217. . ., . ., . . // : . . . . . : , 1999. . 24–25. 218. . ., . ., . . // IV
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SCREEN 11 LINE (40, 100)-(40, 300) LINE (40, 300)-(400, 300) FOR XXX = 40 TO 400 STEP 6 LINE (XXX, 298)-(XXX, 302), 6 NEXT XXX FOR XXX1 = 40 TO 400 STEP 60 LINE (XXX1, 296)-(XXX1, 304), 6 NEXT XXX1 FOR YYY1 = 300 TO 100 STEP -4 LINE (38, YYY1)-(42, YYY1), 7 NEXT YYY1 FOR YYY2 = 300 TO 100 STEP -20 LINE (36, YYY2)-(44, YYY2), 7 NEXT YYY2 LOCATE 20, 4: PRINT "0": LOCATE 20, 29: PRINT "15" LOCATE 20, 50: PRINT "30 ": LOCATE 20, 53: PRINT "FI,grad" LOCATE 13, 2: PRINT "10": LOCATE 7, 2: PRINT "20" LOCATE 6, 2: PRINT "h*10^3,m" KH = 1 DIM NF(KH), X#(7) FOR I = 1 TO KH READ NF(I) 'PRINT NF(I) NEXT I DATA 4000 DATA 4500
,
DATA 5000 DATA 6000 DATA 6500 DATA 7000 DATA 7500 DATA 8000 DATA 8500 20 RK = 15: MMM = 36: RH = .5: EEE = .01 30 K1 = 15: K2 = .015 K1K = 5: K2K = .0035 'PRINT K1 'GOSUB 190 60 NF1 = R14 'NF1 = Q# LOCATE 2, 1: PRINT "NF1="; NF1 70 HH = 6.28 / MMM 90 z1 = K1: z2 = K2 * 10000: PSET (40 + z1 * 12, 300 - z2), 7 FOR I = 1 TO KH NF1 = NF(I) YY1 = K1: YY2 = K2 * 10000 91 FOR AA = 3.14 TO 6.28 STEP HH FOR RRX = 0 TO RK STEP RH RRY = RRX * .0015 RHY = RH * .0015 SS1 = K1 + RRX * COS(AA): SS2 = K2 + RRY * SIN(AA) LOCATE 1, 1: PRINT SS1, SS2 LOCATE 2, 1: PRINT "AA="; AA * 180 / 3.14 LOCATE 3, 1: PRINT "NF="; NF1; "Q="; Q# IF SS1 = 0# THEN GOTO 111 SEQL# = SEQL# + R#(J) * R#(J) 111 NEXT J 444 IF NC = 0 THEN GOTO 313 CALL PROB(1) FOR J = 1 TO NC SEQL# = SEQL# + R#(J) * R#(J) NEXT J 313 SUM#(IN) = SEQL# END SUB SUB WRIT CALL PROB(3) 'PRINT " = "; R#(K9) 'PRINT #1, " = "; R#(K9) FOR J = 1 TO NX 'PRINT " BEKTOP: X("; J; ") = "; X#(J) 'PRINT #1, " BEKTOP: X("; J; ") = "; X#(J) NEXT J IF NC = 0 THEN GOTO 6 CALL PROB(1) FOR J = 1 TO NC 'PRINT " H("; J; "): "; R#(J) 'PRINT #1, " H("; J; "): "; R#(J) NEXT J 6 IF NIC = 0 THEN GOTO 503 CALL PROB(2) FOR J = K7 TO K6 'PRINT " G("; J; "): "; R#(J) 'PRINT #1, " G("; J; "): "; R#(J) NEXT J 503 END SUB 3 > ------------------------------------------------------O EE C O EPEMEHH X: 5 O EE C O O PAH EH B B E: 1).PABEHCTB : 3 2).HEPABEHCTB: 13 BE .O PE .PA MEP E OPM.MHO O PAHH KA: .003 C O O PE .OKOH AH E O CKA: .01 HA A O K ECK X B C EH X( 1 ) = 17 X( 2 ) = 3.000000026077032D-03 X( 3 ) = 3.200000151991844D-02 X( 4 ) = .6000000238418579 X( 5 ) = .3199999928474426 ! Q= 8.91047626339514 / GAM= 5048.469 Q#= 2.062610246156282D-06 ^3/c N= 1452.327011108398 dT= 62.16527083518412 JB= 1.167453E-02 FI= 17 H= .003 D= .032 W= .6 / L= .32 SIGekv= 2.290001E+07 Fprog= 7.374678E-07 FDIFER = .024 SR(N1) = .7174034955390454 ******************************************************* HOMEP C ETA: 2 FDIFER = 8.381973946497475D-04 ! Q= 9.820940261988653 / GAM= 3418.813 Q#= 2.273365801386262D-06 ^3/c N= 1121.288036346436 dT= 41.70574269086681 JB= 8.140317E-03 FI= 16.63561 H= 4.370651E-03 D= 2.948779E-02 W= .5827073 / L= .2904083 SIGekv= 2.280219E+07 Fprog= 5.891075E-07 .
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'*** MINMSCRE *********** ' * '* * '************************************************************* DECLARE SUB FEAS () DECLARE SUB STAR () DECLARE SUB WRIT () DECLARE SUB SUMR () DECLARE SUB PROB (INQ!) DIM SHARED X#(50), X1#(50, 50), X2#(50, 50), R#(100), R1#(100), R2#(100), R3#(100), SUM#(50), F#(50), SR#(50), ROLD#(100), H#(50), FLG#(10), A#(50, 50) COMMON SHARED KIK, NX, NC, NIC, STEP0#, ALFA#, BETA#, GAMA#, IN, INF, FDIFER#, SEQL#, K1, K2, K3, K4, K5, K6, K7, K8, K9, FOLD#, L5, L6, L7, L8, L9, R1A#, R2A#, R3A# OPEN "MINMSCRM.RES" FOR OUTPUT AS #1 PRINT #1, " " PRINT " " PRINT "-----------------------------------------------------------" PRINT #1, " ------------------------------------------------------------" FDIFER# = 1# NX = 3 ' NC = 0 ' NIC = 8 ' SIZE# = .5# ' . . CONVER# = .01# ' ALFA# = 3# BETA# = .5# GAMA# = 3# 10 STEP0# = SIZE# X#(1) = .0025# ' X#(2) = .0031# ' X#(3) = .0069# ' ' CALL PROB(3)
'PRINT " F2IF FDIFER# < CONVER# THEN GOTO 9999 PRINT " >" PRINT #1, " >" PRINT "-----------------------------------------------------------" PRINT #1, " ------------------------------------------------------------" PRINT " O EE C O EPEMEHH X: "; NX PRINT #1, " O EE C O EPEMEHH X: "; NX PRINT " O EE C O O PAH EH B B E: 1).PABEHCTB : "; NC PRINT #1, " O EE C O O PAH EH B B E: 1).PABEHCTB : "; NC PRINT " 2).HEPABEHCTB: "; NIC PRINT #1, " 2).HEPABEHCTB: "; NIC PRINT " BE .O PE .PA MEP E OPM.MHO O PAHH KA: "; SIZE# PRINT #1, " BE .O PE .PA MEP E OPM.MHO O PAHH KA: "; SIZE# PRINT " C O O PE .OKOH AH E O CKA: "; CONVER# PRINT #1, " C O O PE .OKOH AH E O CKA: "; CONVER# K1 = NX + 1 K2 = NX + 2 K3 = NX + 3 K4 = NX + 4 K5 = NX + 5 K6 = NC + NIC K7 = NC + 1 K8 = NC + NIC K9 = K8 + 1 N = NX - NC N1 = N + 1 IF N1 >= 3 THEN GOTO 50 N1 = 3 N=2 50 N2 = N + 2 N3 = N + 3 N4 = N + 4 N5 = N + 5 N6 = N + 6 N7 = N + 7 N8 = N + 8 XN = N XNX = NX XN1 = N1 R1A# = .5# * (SQR(5#) - 1#) R2A# = R1A# * R1A# R3A# = R2A# * R1A# L5 = NX + 5 L6 = NX + 6 L7 = NX + 7 L8 = NX + 8 L9 = NX + 9 ICONT = 1 NCONT = 1 PRINT " HA A O K ECK X B C EH " PRINT #1, " HA A O K ECK X B C EH " FOR J = 1 TO NX PRINT " X("; J; ") = "; X#(J) PRINT #1, " X("; J; ") = "; X#(J) NEXT J FDIFER# = 2# * (NC + 1) * STEP0# FOLD# = FDIFER# IN = N1 CALL SUMR SR#(N1) = SQR(SEQL#) PRINT " FDIFER ="; FDIFER#, " SR(N1) ="; SR#(N1) PRINT #1, " FDIFER ="; FDIFER#, " SR(N1) ="; SR#(N1) IF SR#(N1) < FDIFER# THEN GOTO 341 CALL WRIT INF = N1 STEP0# = .05# * FDIFER# CALL FEAS PRINT " SR(INF) ="; SR#(INF) PRINT #1, " SR(INF) ="; SR#(INF)
PROB"
IF FOLD# < 1E-09 THEN GOTO 80 341 PRINT "************************************************" PRINT #1, " ****************************************" PRINT " HOMEP C ETA:"; ICONT, " FDIFER ="; FDIFER# PRINT #1, " HOMEP C ETA:"; ICONT, "FDIFER ="; FDIFER# CALL WRIT FTER# = R#(K9) STEP1# = STEP0# * (SQR(XNX + 1#) + XNX - 1#) / (XNX * SQR(2#)) STEP2# = STEP0# * (SQR(XNX + 1#) - 1#) / (XNX * SQR(2#)) ETA# = (STEP1# + (XNX - 1#) * STEP2#) / (XNX + 1#) FOR J = 1 TO NX X#(J) = X#(J) - ETA# NEXT J CALL STAR FOR I = 1 TO N1 FOR J = 1 TO NX X2#(I, J) = X1#(I, J) NEXT J NEXT I FOR I = 1 TO N1 IN = I FOR J = 1 TO NX X#(J) = X2#(I, J) NEXT J CALL SUMR SR#(I) = SQR(SEQL#) IF SR#(I) < FDIFER# THEN GOTO 8 CALL FEAS IF FOLD# < 1E-09 THEN GOTO 80 8 CALL PROB(3) F#(I) = R#(K9) NEXT I 1000 STEP0# = .05# * FDIFER# ICONT = ICONT + 1 FH# = F#(1) LHIGH = 1 FOR I = 2 TO N1 IF F#(I) < FH# THEN GOTO 166 FH# = F#(I) LHIGH = I 166 NEXT I 41 FL# = F#(1) LOW = 1 FOR I = 2 TO N1 IF FL# < F#(I) THEN GOTO 177 FL# = F#(I) LOW = I 177 NEXT I FOR J = 1 TO NX X#(J) = X2#(LOW, J) NEXT J IN = LOW CALL SUMR SR#(LOW) = SQR(SEQL#) IF SR#(LOW) < FDIFER# THEN GOTO 87 INF = LOW CALL FEAS IF FOLD# < 1E-09 THEN GOTO 80 CALL PROB(3) F#(LOW) = R#(K9) GOTO 41 87 FOR J = 1 TO NX SUM2# = 0# FOR I = 1 TO N1 SUM2# = SUM2# + X2#(I, J) NEXT I X2#(N2, J) = 1# / XN * (SUM2# - X2#(LHIGH, J)) NEXT J SUM2# = 0#
FOR I = 1 TO N1 FOR J = 1 TO NX SUM2# = SUM2# + (X2#(I, J) - X2#(N2, J)) ^ 2 NEXT J NEXT I FDIFER# = (NC + 1) / XN1 * SQR(SUM2#) IF FDIFER# < FOLD# THEN GOTO 98 FDIFER# = FOLD# GOTO 198 98 FOLD# = FDIFER# 198 FTER# = F#(LOW) PRINT "------------", FDIFER# NCONT = NCONT + 1 IF NCONT < 4 * N1 THEN GOTO 37 IF ICONT < 1500 THEN GOTO 337 FOLD# = .5# * FOLD# 337 NCONT = 0 PRINT "**************************************************" PRINT #1, " *****************************************" PRINT " HOMEP C ETA:"; ICONT, " FDIFER ="; FDIFER# PRINT #1, " HOMEP C ETA:"; ICONT, "FDIFER ="; FDIFER# CALL WRIT 37 IF FDIFER# < CONVER# THEN GOTO 81 IF LHIGH = 1 THEN GOTO 43 FS# = F#(1) LSEC = 1 GOTO 44 43 FS# = F#(2) LSEC = 2 44 FOR I = 1 TO N1 IF LHIGH = I THEN GOTO 18 IF F#(I) < FS# THEN GOTO 18 FS# = F#(I) LSEC = I 18 NEXT I FOR J = 1 TO NX X2#(N3, J) = X2#(N2, J) + ALFA# * (X2#(N2, J) - X2#(LHIGH, J)) X#(J) = X2#(N3, J) NEXT J IN = N3 CALL SUMR SR#(N3) = SQR(SEQL#) IF SR#(N3) < FDIFER# THEN GOTO 82 INF = N3 CALL FEAS IF FOLD# < 1E-09 THEN GOTO 80 82 CALL PROB(3) F#(N3) = R#(K9) IF F#(N3) < F#(LOW) THEN GOTO 84 IF F#(N3) < F#(LSEC) THEN GOTO 92 GOTO 60 92 FOR J = 1 TO NX X2#(LHIGH, J) = X2#(N3, J) NEXT J SR#(LHIGH) = SR#(N3) F#(LHIGH) = F#(N3) GOTO 1000 84 FOR J = 1 TO NX X2#(N4, J) = X2#(N2, J) + GAMA# * (X2#(N3, J) - X2#(N2, J)) X#(J) = X2#(N4, J) NEXT J IN = N4 CALL SUMR SR#(N4) = SQR(SEQL#) IF SR#(N4) < FDIFER# THEN GOTO 25 INF = N4 CALL FEAS IF FOLD# < 1E-09 THEN GOTO 80 25 CALL PROB(3) F#(N4) = R#(K9)
60
64
67
72
68
81
80
IF F#(LOW) < F#(N4) THEN GOTO 92 FOR J = 1 TO NX X2#(LHIGH, J) = X2#(N4, J) NEXT J F#(LHIGH) = F#(N4) SR#(LHIGH) = SR#(N4) GOTO 1000 IF F#(N3) > F#(LHIGH) THEN GOTO 64 FOR J = 1 TO NX X2#(LHIGH, J) = X2#(N3, J) NEXT J FOR J = 1 TO NX X2#(N4, J) = BETA# * X2#(LHIGH, J) + (1# - BETA#) * X2#(N2, J) X#(J) = X2#(N4, J) NEXT J IN = N4 CALL SUMR SR#(N4) = SQR(SEQL#) IF SR#(N4) < FDIFER# THEN GOTO 67 INF = N4 CALL FEAS IF FOLD# < 1E-09 THEN GOTO 80 CALL PROB(3) F#(N4) = R#(K9) IF F#(LHIGH) > F#(N4) THEN GOTO 68 FOR J = 1 TO NX FOR I = 1 TO N1 X2#(I, J) = .5# * (X2#(I, J) + X2#(LOW, J)) NEXT I NEXT J FOR I = 1 TO N1 FOR J = 1 TO NX X#(J) = X2#(I, J) NEXT J IN = I CALL SUMR SR#(I) = SQR(SEQL#) IF SR#(I) < FDIFER# THEN GOTO 72 INF = I CALL FEAS IF FOLD# < 1E-09 THEN GOTO 80 CALL PROB(3) F#(I) = R#(K9) NEXT I GOTO 1000 FOR J = 1 TO NX X2#(LHIGH, J) = X2#(N4, J) NEXT J SR#(LHIGH) = SR#(N4) F#(LHIGH) = F#(N4) GOTO 1000 CLS PRINT "**************************************************" PRINT #1, " *****************************************" PRINT " HOMEP C ETA:"; ICONT, " FDIFER ="; FDIFER# PRINT #1, " HOMEP C ETA:"; ICONT, "FDIFER ="; FDIFER# CALL WRIT PRINT " HA " PRINT #1, " HA " GOTO 10 CLS PRINT "*************************************************" PRINT #1, " *****************************************" PRINT " HOMEP C ETA:"; ICONT, " FDIFER ="; FDIFER# PRINT #1, " HOMEP C ETA:"; ICONT, "FDIFER ="; FDIFER# CALL WRIT PRINT " HET HA A" PRINT #1, " HET HA A" 'SOUND 440, 10 SLEEP 30
GOTO 10 9999 PRINT "---------------------------STOP----------------------------" PRINT #1, " ----------------------------STOP----------------------------" 'SOUND 210, 20 CLOSE END SUB FEAS ALFA# = 1#: BETA# = .5#: GAMA# = 2# XNX = NX ICONT = 0 LCHEK = 0 ICHEK = 0 250 CALL STAR FOR I = 1 TO K1 FOR J = 1 TO NX X#(J) = X1#(I, J) NEXT J IN = I CALL SUMR NEXT I 28 SUMH# = SUM#(1) INDEX = 1 FOR I = 2 TO K1 IF SUM#(I) SUM#(K4) THEN GOTO 601 FOR J = 1 TO NX FOR I = 1 TO K1 X1#(I, J) = .5# * (X1#(I, J) + X1#(KOUNT, J)) NEXT I NEXT J FOR I = 1 TO K1 FOR J = 1 TO NX X#(J) = X1#(I, J) NEXT J IN = I CALL SUMR NEXT I 555 SUML# = SUM#(1) KOUNT = 1 FOR I = 2 TO K1 IF SUML# < SUM#(I) THEN GOTO 233 SUML# = SUM#(I) KOUNT = I 233 NEXT I SR#(INF) = SQR(SUM#(KOUNT)) FOR J = 1 TO NX X#(J) = X1#(KOUNT, J) NEXT J GOTO 26 601 FOR J = 1 TO NX X1#(INDEX, J) = X1#(K4, J) NEXT J SUM#(INDEX) = SUM#(K4) GOTO 555 16 FOR J = 1 TO NX X1#(INDEX, J) = X1#(K4, J) X#(J) = X1#(INDEX, J) NEXT J SUM#(INDEX) = SUM#(K4) SR#(INF) = SQR(SUM#(K4)) GOTO 26 14 FOR J = 1 TO NX X1#(INDEX, J) = X1#(K3, J) X#(J) = X1#(INDEX, J) NEXT J SUM#(INDEX) = SUM#(K3) SR#(INF) = SQR(SUM#(K3)) 26 ICONT = ICONT + 1 FOR J = 1 TO NX X2#(INF, J) = X#(J) NEXT J IF ICONT < (2 * K1) THEN GOTO 500 ICONT = 0 FOR J = 1 TO NX X#(J) = X1#(K2, J) NEXT J IN = K2 CALL SUMR DIFER# = 0# FOR I = 1 TO K1 DIFER# = DIFER# + (SUM#(I) - SUM#(K2)) ^ 2 NEXT I DIFER# = 1# / (K7 * XNX) * SQR(DIFER#) IF DIFER# > 1E-14 THEN GOTO 500 IN = K1 STEP0# = 20# * FDIFER# CALL SUMR SR#(INF) = SQR(SEQL#)
FOR J = 1 TO NX X1#(K1, J) = X#(J) NEXT J FOR J = 1 TO NX FACTOR# = 1# X#(J) = X1#(K1, J) + FACTOR# * STEP0# X1#(L9, J) = X#(J) IN = L9 CALL SUMR X#(J) = X1#(K1, J) - FACTOR# * STEP0# X1#(L5, J) = X#(J) IN = L5 CALL SUMR 56 IF SUM#(L9) < SUM#(K1) THEN GOTO 54 IF SUM#(L5) < SUM#(K1) THEN GOTO 55 GOTO 97 54 X1#(L5, J) = X1#(K1, J) SUM#(L5) = SUM#(K1) X1#(K1, J) = X1#(L9, J) SUM#(K1) = SUM#(L9) FACTOR# = FACTOR# + 1# X#(J) = X1#(K1, J) + FACTOR# * STEP0# IN = L9 CALL SUMR GOTO 56 55 X1#(L9, J) = X1#(K1, J) SUM#(L9) = SUM#(K1) X1#(K1, J) = X1#(L5, J) SUM#(K1) = SUM#(L5) FACTOR# = FACTOR# + 1# X#(J) = X1#(K1, J) - FACTOR# * STEP0# IN = L5 CALL SUMR GOTO 56 97 H#(J) = X1#(L9, J) - X1#(L5, J) X1#(L6, J) = X1#(L5, J) + H#(J) * R1A# X#(J) = X1#(L6, J) IN = L6 CALL SUMR X1#(L7, J) = X1#(L5, J) + H#(J) * R2A# X#(J) = X1#(L7, J) IN = L7 CALL SUMR IF SUM#(L6) > SUM#(L7) THEN GOTO 688 X1#(L8, J) = X1#(L5, J) + (1# - R3A#) * H#(J) X1#(L5, J) = X1#(L7, J) X#(J) = X1#(L8, J) IN = L8 CALL SUMR IF SUM#(L8) > SUM#(L6) THEN GOTO 76 X1#(L5, J) = X1#(L6, J) SUM#(L5) = SUM#(L6) GOTO 75 76 X1#(L9, J) = X1#(L8, J) SUM#(L9) = SUM#(L8) GOTO 75 688 X1#(L9, J) = X1#(L6, J) X1#(L8, J) = X1#(L5, J) + R3A# * H#(J) X#(J) = X1#(L8, J) IN = L8 CALL SUMR STEP0# = SIZE# SUM#(L9) = SUM#(L6) IF SUM#(L7) > SUM#(L8) THEN GOTO 71 X1#(L5, J) = X1#(L8, J) SUM#(L5) = SUM#(L8) GOTO 75 71 X1#(L9, J) = X1#(L7, J) SUM#(L9) = SUM#(L7) 75 IF ABS(X1#(L9, J) - X1#(L5, J)) > .01# * FDIFER# THEN GOTO 97
X1#(K1, J) = X1#(L7, J) X#(J) = X1#(L7, J) SUM#(K1) = SUM#(L5) SR#(INF) = SQR(SUM#(K1)) IF SR#(INF) < FDIFER# THEN GOTO 760 NEXT J ICHEK = ICHEK + 1 STEP0# = FDIFER# IF ICHEK FDIFER# THEN GOTO 28 IF SR#(INF) > 0# THEN GOTO 35 CALL PROB(3) FINT# = R#(K9) FOR J = 1 TO NX X#(J) = X2#(INF, J) NEXT J CALL PROB(2) FOR J = K7 TO K8 R1#(J) = R#(J) NEXT J FOR J = 1 TO NX X#(J) = X1#(KOUNT, J) NEXT J CALL PROB(2) FOR J = K7 TO K8 R3#(J) = R#(J) NEXT J FOR J = 1 TO NX H#(J) = X1#(KOUNT, J) - X2#(INF, J) X#(J) = X2#(INF, J) + .5# * H#(J) NEXT J CALL PROB(2) FLG#(1) = 0# FLG#(2) = 0# FLG#(3) = 0# FOR J = K7 TO K8 IF R3#(J) >= 0 THEN GOTO 404 FLG#(1) = FLG#(1) + R1#(J) * R1#(J) FLG#(2) = FLG#(2) + R#(J) * R#(J) FLG#(3) = FLG#(3) + R3#(J) * R3#(J) 404 NEXT J SR#(INF) = SQR(FLG#(1)) IF SR#(INF) < FDIFER# THEN GOTO 35 ALFA1# = FLG#(1) - 2# * FLG#(2) + FLG#(3) BETA1# = 3# * FLG#(1) - 4# * FLG#(2) + FLG#(3) RATIO# = BETA1# / (4# * ALFA1#) FOR J = 1 TO NX X#(J) = X2#(INF, J) + H#(J) * RATIO# NEXT J IN = INF CALL SUMR SR#(INF) = SQR(SEQL#) IF SR#(INF) < FDIFER# THEN GOTO 465 FOR I = 1 TO 20 FOR J = 1 TO NX X#(J) = X#(J) - .05# * H#(J)
NEXT J CALL SUMR SR#(INF) = SQR(SEQL#) IF SR#(INF) < FDIFER# THEN GOTO 465 NEXT I 465 CALL PROB(3) IF FINT# > R#(K9) THEN GOTO 46 SR#(INF) = 0# GOTO 35 46 FOR J = 1 TO NX X2#(INF, J) = X#(J) NEXT J 35 FOR J = 1 TO NX X#(J) = X2#(INF, J) NEXT J END SUB SUB PROB (INQ) '" ,[ ]" NNN = 10' ( ) NK = 10 ' ( ) PP = 50000000: DP = PP / NK '" [ ]" LL0 = .016: R1 = .016: TT = .032 LL = TT * NK: BE = (17 * 3.14 / 180) '" [ ] . " SIGD = 325000000: FF = .2 '" [ ]" WD = .01 * 2 * R1 '" [ / ^3], [ ] . .[ / ^2]" RO = 7850: EE = 2E+11: GG = 9.81 '" , , " Q = RO * GG * 3.14 / LL * ((R1 - X#(1)) ^ 2 * LL + 2 * (R1 - X#(1) / 2) / COS(BE) * X#(1) * X#(2) * NK - X#(3) ^ 2 * LL) FFP = 3.14 * ((R1 - X#(1)) ^ 2 - (X#(3)) ^ 2) J2 = 3.14 * (R1 - X#(1)) ^ 4 / 4 * (1 - (X#(3) / (R1 - X#(1))) ^ 4) WW0 = 3.14 * (R1 - X#(1)) ^ 3 / 2 * (1 - (X#(3) / (R1 - X#(1))) ^ 4) 'LL1 = (2 * 3.14 * (R1 - X#(1)) ^ 4 * WD * EE / Q) ^ .25 PRINT "Q="; Q; "LL="; LL; "WD="; WD PRINT "X#(1)="; X#(1); "X#(2)="; X#(2); "X#(3)="; X#(3) PRINT #1, "Q="; Q; "LL="; LL; "WD="; WD PRINT #1, "X#(1)="; X#(1); "X#(2)="; X#(2); "X#(3)="; X#(3) '" F5" MYS0 = 0: MYS1 = 0: MYS2 = 0: QYS1 = 0: QYS2 = 0: QYS3 = 0 FOR I = 1 TO NK - 1 XI = (2 * I - 1) * TT / 2 IF I