Математическое моделирование применительно к литейному производству. Черный А.А. - 6 стр.

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(
)
2
n
m
n2
m
rn
m
r
m
n
m
m
xx
xxx
a
−
−⋅
=
+
; (3)
(
)
n
mm
r
mm
xaxc ⋅+−= ; (4)
(
)
2
2 n
m
n
m
sn
m
s
m
n
m
m
xx
xxx
p
−
−⋅
=
+
)xxx(Pxxxt
rn
m
r
m
n
mm
sr
m
s
m
r
mm
++
−⋅+−⋅=
1
]x)x[(Pa)xxx(at
n
m
n
mmm
sn
m
s
m
n
mmm
22
2
−+−⋅=
+
)xxx(a)x(xt
r
m
n
m
rn
mm
r
m
r
mm
−−+−=
+
2
22
3
])x(x[at
tt
d
n
m
n
mmm
mm
m
222
3
21
−⋅+
+
=
(5)
mmmm
Pade +⋅= (6)
(
)
n
mm
r
mm
s
mm
xexdxf ⋅+⋅+−= (7)
n
mm
r
mm
xaxt ⋅+=
4
n
mm
rn
m
n
mmm
xaxxtt
2
45
⋅−−⋅=
+
mm
r
mm
rn
mm
r
mm
atxtxaxt ⋅−⋅−⋅+=
+
54
2
6
sn
mm
sr
mmm
s
mmm
xaxPtxtt
++
⋅−−⋅+⋅=
547
(
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2
2 n
m
n
m
wn
m
w
m
n
m
m
xx
xxx
z
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=
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mm
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w
mmmmm
xaxxtztt
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⋅−−⋅+⋅=
458
sn
mm
sr
mm
s
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xexdxt
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⋅+⋅+=
2
9
rn
mm
r
mm
sr
mm
xexdxt
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⋅+⋅+=
2
10
n
mm
rn
mm
sn
mm
xexdxt
2
11
⋅+⋅+=
++
n
mm
r
mm
s
mm
xexdxt ⋅+⋅+=
12
wn
mm
wr
mm
ws
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xexdxt
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13
       x nm ⋅ x rm − x nm+ r
am =                              ;                                          (3)
         x 2mn   −   ( )
                     x nm
                            2




          (
c m = − x rm + a m ⋅ x nm         )   ;                                      (4)

         x mn ⋅ x ms − x mn + s
 pm =
                     ( )
           x m2 n − x mn
                            2


t m1 = x mr ⋅ x ms − x rm+ s + Pm ( x mn ⋅ x mr − x mn+ r )


t m 2 = a m ( x mn ⋅ x ms − x nm+ s ) + a m Pm [( x mn )2 − x m2 n ]


t m3 = x m2 r − ( x mr ) 2 + 2a m ( x mn + r − x mn − x mr )

                     t m1 + t m 2
dm =                                                                    (5)
    t m3 + a m2 ⋅ [ x m2 n − ( x mn )2 ]
 em = d m ⋅ a m + Pm                                                         (6)
           (
 f m = − x ms + d m ⋅ x mr + em ⋅ x mn      )                          (7)

 t m 4 = x mr + a m ⋅ x mn
t m5 = t m 4 ⋅ x mn − x mn + r − a m ⋅ x m2 n
t m 6 = x m2 r +a m ⋅ x mn+ r − t m 4 ⋅ x mr − t m5 ⋅ a m
t m 7 = t m 4 ⋅ x ms +t m5 ⋅ Pm − x mr + s − a m ⋅ x mn+ s
        x mn ⋅ x mw − x mn + w
zm =
                     ( )
           x m2 n − x mn
                            2


t m8 = t m5 ⋅ z m + t m 4 ⋅ x mw − x mr − w −a m ⋅ x mn + w
t m9 = x m2 s + d m ⋅ x mr + s + em ⋅ x mn + s
t m10 = x mr + s + d m ⋅ x m2 r + em ⋅ x mn+ r
t m11 = x mn+ s + d m ⋅ x mn+ r + em ⋅ x m2 n
t m12 = x ms + d m ⋅ x mr + em ⋅ x mn
t m13 = x ms + w + d m ⋅ x mr + w + em ⋅ x mn + w

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