close

Вход

Забыли?

вход по аккаунту

?

Оптимальная круговая расстановка станков в поточном производстве.

код для вставкиСкачать
2004 BECTHHK
CAHKT-l7ETEPLiYPrCKOrO
YHNBEPCNTETA Cep. 5. B H ~ 3. (342 2 1 )
0IITElMAJIbHA.A KPWOBAII PACCTAHOBICA CTAHKOB
B IIOTOYHOM IIPOEl3BOflCTBE
P~CCMOT~AM
MHOrOnPenMeTHOe
nPOH3BOACTBO
KHMH MaPIIIPYTaMH H3rOTOBJIeHHR HpeAMeTOB.
B 3TUX
C pa3HOHaIIpaBJIeHHbIMH TeXHOJlOrHYeCYCJIOBIUIX B03HHKaeT 3 W a Z I a PaCCTaHOBKU
( p a 3 ~ e U e H ~ XH, ~ ~ H ~ Z I ~ HCTaHKOB
UR)
H a H M e I O u H e C R B HallHLIHH n n O 4 W K H
( M ~ c T ~B )KIKOM-TO
OrpaHHYeHHOM npOCTpaHCTBe TaK, ' . I T O ~ ~MHHHMH3HPOBaTb
I
C Y M M ~ P H ~~I 3
~ ~0 0 6 0 (pa6o~y
~ 0 ~ IIO
nepeMeUeHHm B
namu
npoqecce
H~~OTOBJI~HH
BR
cex npenMeToB
~pyna).%a 3ma~1a
oTHocmca
Hsxe
H3BOnHTeJIbHOCTb H 3 a T p a T b I @YHKIJHOHNPOB~HAR B C ~ # CHCTeMbI M I W H H .
06npo-
K
n p o e m p o s a H H n ~ ~ O H ~ B O ~ C T B CHc-reMbI.
~ H H O ~ ~Ee p e l u e H u e BO M H o r o M O n p e n e n x e T
IIpenJ'IXaeTCH
TOZIHOe PeLIIeHHe 3~0fi
3 m a Z I H A n R Y C J I O B H ~IIOTOYHOFO
~
lTpOH3BOnCTBa.
B
MHOrOYHCneHHbIX
pa6o~ax,IlOCBRweHHbM 3~0fi3 a a z l e , npe.4JlamHCb P W H s H b I e 3BpHsnw csene~ae6onee o6wefi 3ma.r~(a m e m o npw norry-
m q e c K H e , I I ~ I ~ ~ J I H X C ~pewearn'
HH~I~
U e H H H I l e T e n b B TeXHOJIOTHSeCKEiX MaPJIIPYTaX H3rOrOBJIeHIUI ~ P ~ ~ M ~ T KO 3Bm )a r I e 0 pa3MbIKaHHH KOHTYPOB B rpa@e,2peluae~ofiB e C b M a
auefi cmne y n a n o c b ~aitmin o c r a ~ ~ wx oe
TpyAOeMKHM MeTOnOM BeTBefi H V a H H I J .
~ ~ ~~e o
o 6ex o m o e
ycnome o
r
n
a
~
B
HaCTO-
~ HbC K~O MmO ~ ~
nepeCTaHOBKI3 HOMePOB CTaHKOB, KOTOpOe H n03BOJIIIeT ~@@KIMBHo H a X O m BCe OrrruMallbHble
n e p e m o s m m / r e ~n e w p a ~e60mluo1-0wcna n o n y m b m n e p e c r a H o B o K . Ta~ofiq u e M
snepme 6 b m n p e n n o x e H n p o ~k.~ .B. POM~HOBCKMM
~ J L Rpernewin w a w o y e ~ a ~ ~ e i i . ~
- A-p 3KOH. HaYK, ~ ~ O @ C C O P K a @ ~ p b l SKOHOMH~~CKORK H ~ ~ P H ~ T H KCn6l-y.
H
O K O H ~ U J ~MBTCMBTHKO~ e x a ~ u r e c ~+a~ynbn f i re^ Cn6l-Y (1964) H acnnpamypy ~a@npu S K O H O M H S ~ C K O ~K~ H ~ ~ P H ~ T H KCII6l-Y
H
(1972).
B Y ~ u x p c m ep a h e r c 1965 r. K m n u n m K y w nncceln;lunm ~ ~ U I H T BH ~1973 r., ~ O K T O ~ C K ~-I OB 1989 r.
cTa)KHp~BaJlcJl B Y H H B e p c H E T a X @ P ~ H U H H (1976). 0 6 J l a C T b HaYYHMX H H R p C O B - ~ P O H ~ B ~ A C T B ~ M
H eHH~e M
~M
# eUT,
r n 6 ~ a~B eT O M m 3 H p O B a H H b l e npOH3BOllCTBa. MHKPO3KOHOMHKa. A B T 0 p 6 O n e e 30 HaYSHblX r r y 6 n ~ ~ a s u f iB, TOM 'IHCne
OnHOrO y q e 6 ~ o mnoco6m C VH@M
MHHHCreJXTBa (B C O ~ B T O P C T B ~H) o J ~ H o M
~ ~O H O T ~ ~ + W H .
n o I I p e n M e T y j-r0 0' = 1: n)
cnenymuae x a p a K T e p w m K a :
HaUMeHOBaHHX (&I'M KPaTKOCTU,
j-MY
IIpen~eTy)H3BeCTHbI
4- n p o r p a M M a B b r n y c K a ( m.)H a n n a ~ u p y e ~ bnepson;
~ i i
(TM),- T ~ x H o J ' I o ~ U Y ~ C K UM~a~p w p y T U3rOTOBneHHX.
T e x ~ o n o r u ~ e c ~ kMi aep r U p y m n p e n M m B
n p e n n o n m x x o6uero suna,
T.e. XBJIXIOTCX
pa3HbIMU ( p a 3 ~ 0 ~ a n p a B n e ~ ~ b 1 ~ ~ ) .
3 ~ a T ~e x H~o n oer n s e c K o r o M a p r U p y T a n 3 r o ~ o ~ n e ~npennonaram
ux
npeme B c e r o s ~ m u e
m, - m u H a (ThfI,, T.e. o6uee K o n a s e c - r B o ( ~ e x ~ o n o r a ~ e c ~onepauuii,
ux)
H ~ o ~ x o ~ U M &llR
~ I XA3rOTOBJIeHElrr l l p e n ~ e ~.a j
C Y H T ~ ~YTO
M , ~ 6 n ~ p y 1 0 w e rOo~ O P Y A O B ~ H U XH a O n e p a U H X X HeT, T.e.
BbIlTOnHeHWl
KZ~XJ(O~~
O n e p a q U k I HMeeTCX TOnbKO OAHH (((cBo~~)))
CTIHOK, U T O r A a m XBJIXeTCX OAHOBPeMeHHO U
KOnUYeCTBOM CTaHKOB, UMeK)UUXCX H a Mll.JI. ~ P 3TOM
U
A O l l y U e H H U 3 a A a T b TeXHOJIOrUYeCKUe
ero
AJIUH~I:
MaplrrpyTbI ITpeAMeTOB MOXHO C n O M O u b I O YKa3aHWI,
0IIepauEiii K CTaHKaM.
i-x no
B
3TOM CJTyYae U3BeCTeH
n o p m ~ B
y TexHonormecKoM M a p w p p e
Aanee c q n T a e M ,
YTO
H a n p H M e p , IIpUBX3KH UX n P e n M e T O -
S - H O M e p cTaHKa, H a KOTOPOM BbIIIOJIHXeTCX
r/
onepaunx j-ro
(15s.. < m , i = I: m, ,
npenMeTa
x x ~ o n o r ~ ~ eMca p~r r r~p yiTi nm6oro
I/ -
n p e n M e T a H e u M e e T n m e n b , T.e.
BCe H ~ O ~ X O ~ U
mM
X ~H3rOTOBJIeHRX
I ~
n p e n M e T a O n e p a u H A BbInOJIHRIOTCX ( C T ~ H K UU C ~ I O J I ~ ~ Y I O T C X )
no OnHOMy pa3y. M3 3 T O r O H ~ O ~ X O ~ MBbITeKaeT,
MO
YTO mj 5 m, n p U 3TOM eCJIH &I'M U3TOTOBJIeHUX
H e K o T o p o r o n p e n h i e ~ ja ~ p e 6 y e ~ B
c xa x n o n H m b B c e m onepausii, TO mj = m , a ecna H e K o T o p a I e ~3
HUX nPOnYCKaKlTCX ( H e T ~ ~ ~ Y I O T C X )TO
, mj < m. OTC~TCTBA~
IIeTeJ'Ib B TeXHOJIOrHYeCKUX
MapIlIpyTaX n p e A M e T O B @ 0 p ~ a J I b d @ ~ 0 3 H a Y a e TYTO
,
S.. # S . n U i # k , T.e. (TM),. e C T b
'J
u3 m no mi (j= 1: n).
o6ueii U H @ O ~ M ~ ~ HAJIX
H
M m
b P
HeKoTopoe p a 3 M e u e H n e
~OMHMO
TOG
UMeeTCX
TZWXe
H
CJle~IOII@A
ran.
AOnOnHUTenbHaX HH@OPMB~UR,XBJlXIOI4aJICX C ~ ~ ~ H @ H Y ~AJIX
C K O ~ ~
qj- w ~ y ~ k bB~ ~ij-TO
Ci
n p e n M e T a 0' = 1: n).
E c n ~B I I p O u e C C e U3rOTOBJleHHX n p e n M e T a er0 BeC MeHXeTCX 3 H a Y k i T W b H 0 , TO B KaYeCTBe
ero seca n p u H H M a e M ~ e ~ ~
cpen~uii
l i i B npoqecce ero u 3 r o ~ o ~ n e ~sec.
nx
C Y H T ~ ~YTO
M ,nrfn O C H u e H a KPYrOBbIM ( ~ . e r.O P U 3 0 H T a n b H O ~ ~ M K H ~ T ~ KI MO ) H B ~ ~ ~ ~
J(JIHH0fi L MeTPOB, H2WlpaBneHUe ABUXeHUX ( B ~ ~ U ~ H H X
KOTOpOrO
)
U3BeCTH0, H W H M e p , no
saco~oiic r p e n K e . no nepme-rpy neH-rbx ~ o ~ s e i i e pu Ma e e T c x m + l n n o u a n K a , ~3 KOTOPLIX o n H a
( 3 ~ 1 y ~ e p y ee
e ~ H Y ~ ~ M i: = 0) 3 a p a H e e OTBOAHTCR n O n K n a O B y H , ( K O M ~ J I ~ K T O B O Y H Y I O
I U I ~ O B ~ I O ) ,a o c T a n b H b I e (i = 1 : m) - mx p a c n o n o x e H m H a ~ n memutixcx
x
m CT~HKOB
( ~ C T ~ C T B ~ H Hno
O , OAHOMY H a KaX,40fi) B K~KOM-JIki60 IlOPIInKe.
Aanee, c s m a e M , YTO n e p e A H a s a n o M H ~ ~ O T O B J I ~ HBUc e~x r r p e n M e T o B ux ~ ~ O T O B K H
H a X O m C X B K ~ ~ o B oa ~H3rOTOBJIeHHbIe
~ ,
A 3 HRX V e A M e T b I I I O c l y n a I O T B H e e Xe. E y n e ~
CYHTaTb
ee YCnOBHbIM CTaHKOM, K o T O P ~ I ~3~a H y M e p y e M H y n e M , H nOIIOJIHHM HM TeXHOJIOrHYeCKHe
nocmanos~a3adavu
B ~ e n e0 6~0 3 ~ a Y e ~ k u r .
si - H o M e p c T a H K a , y c m a s n a s a e M o r o H a i-m nnoum~y(15 si5 m, i = I :m; si # sk npa i # k).
no I l n O U a n K a M . K o n u ~ e c r ~TaKHX
o
nOPRnKOB ( ~ ~ P ~ C T ~ H O
P aB
B HOO K
m!)
F,(P) - K o n u . r e c r B o O ~ O P O T O B(BUTKOB) ~ o ~ s e i i e pHa ,~ O ~ X O A U MAJU
O ~ n o n H o r o usro~o~neHUA j-ro n p e n M e T a (j= 1 : n), ecnu c T a H m i p a c c T a B n e H b 1 no n n o q a p X a M B n o p n n l c e P. OY~BWHO,
OHO y n o B n e m o p H e T H e p a B e H c T B a M : 1 IF,(P) Im, ( j = I : n ). A B H O ~ (a~anu-rurec~oro)
O
B b l p W e H U R AJ'IH BeJlUYHHbl F,(P) H e C y U e C T B y e T . O ~ H ~AJlH
K OK O H K ~ ~ Tn aHp bOl ~n e~p e c T a H O B O K
IlOnCYeT ee H e B b l 3 b l B a e T ~ ~ T P Y ~ H ~ H H ~
I l p u ~ e pp a c s e T a F,(P).
n y C T b H a n U H U U HMeeTCR 5 CTaHKOB (m = 5), KOTOPble P a C C T a B n e H b l no I l J l O U m K a M B
n o p x n K e P = (3, 1, 4, 5, 2), a (TM), = (4, 2, 3, 5, 1). Torna H a n e p s o M B u T K e ~ o ~ ~ e i iij-j e p a
n p e n M e T np0fineT o 6 p a 6 0 ~ ~
TO
yn b K O H a CTaHKaX 4 U 2, H a BTOPOM BMTKe - H a CTaHKaX 3 H 5 U Ha
T p e T b e M BUTKe - H a CTaHKe 1. tam^ O ~ P ~ O M
4(P)
,
= 3. (Bo B T O P O ~n~e p e C T a H O B K e (4,2,3,5, 1)
HMelOTCH A B e T a K H a 3 b l B a e M b l e r J l a B H b l e MHBePCHU no OTHOllleHUK) K nep~0fin e p e C T a H O B K e
(3, 1, 4, 5, 2) - nsa p n n o ~CTORUUX B ~ e i Hi o M e p a 2,3 u 5,1, u M e m q u x n p m u B o n o n o x w o e
y n O p R n O k l e H U e no C p a B H e H U H , C n e p B 0 i i n e p e C T a ~ o B K o f i ,- U, CJleAOBZWWIbHO, KOnMYeCTBO ~pe6ym U U X C R BUTKOB, OYeBU,UHO H a e n U H H U Y 60nbmee KOnHYeCTBa rJlaBHblX H H B ~ P C U ~
P a~B, H O TpeM.)
&In c y M M a p H o r o ( ~ . e no
. B c e M n p e n ~ m rpy30060po~a
~)
( ~ . e p. a 6 0 ~ b lno n e p e M e u e H u m
BCeX l"py30B, CM)
H a n H H H U U M e e M C n e p y m w t o O Y e B W H y I o @ 0 p ~ y J I y : Lx'J.=lq, N j F , (P).
PlCCTliHOBKU CTaHKOB
L H e BJlUXeT H a OllTUMM3aUUK), TO B ~anb~efilllehl
6 y n e ~PaCCMaTpHBaTb
efi U e J l e B y K l @YHKUUH) ( C Y M M ~ ~ KT-BMTKU):
H ~ I ~
F(P) = C';=, q l N ,FJ (PI-
T a K KaK MHOHCUTeJlb
PaBHOCUnbHyH)
Aslfl
H e e M O X e T 6b1Tb n0Jl)'YeHO
U RBHOe ( ~ H Z U ~ U T U Y ~ C K B
O b~ l)p a X e H U e Y e p e 3 UCXOnHble DaHHble,
6ynm n p U B e n e H 0 HH)Ke.
no n n O U m K a M TaK, Y T O ~ ~ I
TWM o 6 p m o ~ ,~ p e 6 y e ~ cHa ~ T U
T.e. H e H C n O n b 3 Y H ) U e e KOnUYeCTBO BUTKOB, KOTOPOe B n e p B b l e
K ~ yXe
K
yKa3blBaJlOCb B b I U e ,
~ p e 6 y e ~ cPaCCTaBMTb
n
C Y M M ~ P H ~TI ~~Y~ ~ O O ~ O P OHTa JIMHHU 6 b ~ 1MUHUMZUlbHbIM.
nepecraHoBrty
P' : F(P> =
rnFF(P).
CTaHlul
Mampuya zpy3onomorcos
&Is HaXOlKJleHUH
RBHOI'O
IlpeABapUTWIbHO nOcTpOUM
B b l P a X e H U X AJlR
( ~ OCHOBe
a
40-u U
PellleHUX. p a ~ ~ ~ a l ' p U B a e ~3aAaYU
0fi
Y K m a H H b I X B b l l u e HCX0,QHblX ~ ~ H H ~ TaK
I X )Ha3blBaeMYtO
MaTpuuy T ~ ~ ~ O ~ O T O K
( ~O. Be B. e c o B n e p e ~ e u a e ~ bnpeme-ro~)
~ x
c K w o r o mama H a ~ w b r - j i
npyroii Q = I I q kr I Im+, , ~ J I ~ M ~ qHkrT K O T O P O ~ ~0 3 ~ a ~ rap ye 3~o n 0 ~ 0(~.e.
~ Bec nepeMeuaeMbn
n p e n ~ m o ~c )k-ro m K a H a r-ii ~ H O K(k , r = 0: m) B T e y e H u e n n m o B o r o nepuona n
B T e x H o n o m Y e c m x M a p u l p y T a X KOTOP~IX 3a ~ K O kM cpa3y
cnepyercrmonr: D, = { j :sg = k , s i + , , , = r ). Cnenoaa~enb~o,
~ a ~ p uQ
u aRBIUI~TCX
M H o x e c r B o B c e x npe,weTOB,
M o X H O 3 a M e T U T b T a m e , YTO
TeX npe,4MeTOB,
= {j : k
E
06e 3TU C y M M b l
B TeXHOnOTUYeCKHe
06e C y M M b I ( I )
PaBHbI
CjEq
Qj
j
,me D
M a P U l P Y T b l KOTOPbIX B X O M T
(TM), }. B y a m o m , ecnu k-ii
IlpenMeTOB, T O
PaBHbl
k-ri
,
e C T b MHOXeCTBO
CTIHOK,
T.e.
D k=
~ H O BXOAMT
K
B T e x H o n o r u q e c w i e Mapu..pyTbl B c e x
Cy=lq j N j .
~ O K = ~ MI l O C T P O e H U e M a T p U U b l CPY30nOTOKOB JlJlX KOHKPeTHbIX YMCJleHHblX naHHbIX.
n p l ~ ~ e pnyCTb
l.
)lJlR n R T U I l p e n M e T O B (n = 5 ) U M e e M C J ' l e ~ y l O U W e I l p O r p a M M b l BblIlyCKa U
m q w b l e seca ( ~ a 6 n .1, crpow 1-3). P a c c r u ~ b ~ s asec
e~ H a nporpaMMy Kamaoro npenMeTa
(~a6n.1,T O K a 4). Aanee, n y C T b B u e X e HMeeTCR lllecTb CTaHKOB, T.e. M O Y T 6 b l ~ bB b l n O n H e H b l
l r r e c T b onepauuli ( m = 6 ), u 3 m a ~ b T
1 exHonoruvecwie MapwpyTbl ( ~ o ~ e p
sa.. ~ H K O mx
B
B
C IlOMOUbH)
1. D X
MaTpHubl
Q nOCTPOUM pSe CJleAytOrUUe M a T p H U b l U OTMeTUM HX C B O ~ ~ C T B ~ .
= (S, ,S Z , . . . , Sf , . . . ,S,) nOCTpOHM MaTpUlQ'
IYepecTaHOBKM ( H O M ~ P O BC T ~ ~ H K O BP
)
s
4sao
qs,s,
0
...
4s,s,
S
qs,o
%,st
9s,s2
...
qs;s,
.
.
. 2
,
.
.
Torna pemaeMyro s a n a ~ yM
Bwe
+ma,
O ~ 3anuca~b
O
B
-
...
qs,sm
= QP.
qs,s-
Bu.qe Qp + min ma
-
B
oseeumo paBHocllnbaoM
CMMBOn Q,, 03HaYam CyMMy 3JleMeHTOB BepXHe8 TPeyroJIbHofi
2. A = Q - Q' = II At Ilm+, ( k, r = 0 : 11I ), T.e. W 3 KwOrO 3JleMeHTa MaTPHUbl Q BblYTeM
C H M M ~ T P U eMy
' I H ~3neMeHT
I~~
(Q'- TPaHCnOHUPOBaHHaR MaTPI-iUa Q ). MaTpuqa A XBJljIeTCR,
OYeB-0,
KOCOCUMM~TPHY~CKO~~:
(Akr = - Ark '). B ,Qal'lbHefiUle~
3Ta MaTpUUa 6yne-r HrPaTb
OCHOBHYH) ponb npu perueHuu noc-ramen~oiisanaqu.
n o MaTpuue A Toxe n o q o u M c o o ~ s m ~ y t o m y Ma.rpuuy
m
A, (A, = ( Q - Q ') ), T.e.
nonyqamq'mcx u 3 , ~ a ~ p u uAb r pacnonoxeHueM ee c r p o ~u cron6uo~B nopxme P ( m u Bce
,,
~ a q u u e i i . Torna peruaeMym sanasy, osesuneo,
MOXHO
c
r e m a o 6 u ~ o e mnonaramx so = 0 ; npu k=O : o l . ;
3anucan ewe u
B
cnenymruux
= 0 (8, cnenoBaTenbHo, (2)
I
I
!
'
,
sepx~uiiyron, .mm H M a q u q a A p , u
cnenymqek (csepxy) nocne r n a ~ ~ nuaro~anu.
ok
npasblii
n e ~ b ~ iHiU X H U ~ ~yron
~ o ~ o p o ni ie m T
Ha
3nehienmap~oenpeobpmosaiiue nepecma~oa~u
Onpedene~ue.3 n e ~ e n ~ a p nnpeo6pa30san~e~
b1~
nepecTaHoBKu Ha3oseM nepeMeHy B ~ e i i
M e c r a M H npyr C n p y r O M JIByX ~ a ~ u x - n u 6COCenHUX
0
HOMePOB.
ACHO, 'ITO 3 T 0 npeo6pa3osa~ueKS1K-TO nOBnUXeT H a KOJlHqeCTBO BUTKOB JlJU K~KUX-nu60
nPeAMeTOB H, COOTBeTCTBeHHO, H a 3 H a Y e H U e UeJleBofi ~ Y H K U W U
M M ~ H H OC l l p a B e ~ U B O
cnenytoqee y ~ e p m s e ~ u enamuee
,5
o m o B p e M e H H o u uw.repnperauuto ~ ~ ~ M ~ HMT ~O HB U A
~. I
Ymeepxdenuel. npu ~ J I ~ M ~ H T ~ npeo6pa30sa~uu
~ H O M
n e p e c r a H o s K u P=(. . . , k , r ,
)
B n e p e m o B K y P' = (. . . , r , k , . . . ) s ~ a s e ~ uurn-u
e
U ~ M ~ H U T CHX a s e n u s u ~ yA b , T.e. uMeeM:
F(P3 = F(P) + A h .
(urn).
. ..
C n p a B e ~ U ~ o C =TObr 0
yTBePX,lJeHwR
B b m K a e T U 3 TOrO, q T 0 n p U YKa3WHOM 3neMeHTapHOM
npeo6pa30~a~uu
nepeCTaHOBKU P KOJlUqecTBO BUTKOB:
- y B e n u r u T c r H a enuauuy m~B c e x n p e n M e m B u3 M H O x e C T B a Dk, u, C n e n O s a T e n b H O ,
3 ~ a ~ t e ~ u e
-
OCTaHeTcR HeH3MeHHbIM )&ilA BCeX OCTanbHblX ' n p e m e M B ( ~ . e . T e X IIPe,llMeTOB,
B
T e m o n o r u q e c m x M a p u p y T a x KOTOP~IX H o M e p k d u n u r O T C ~ T C T B ~ ~unu
T
~ T HH o M e p a H e
RBnRKYrCI C M ~ K H ~ I M U ) .
B p e 3 y n b ~ a ~ e - 3 ~ a r 4e 0~ -u ew m M e H u T c n
9, - q,.k ,T.e. Ab .
Ha BenuruHy
H o M e p o B n p e m e m B y e T x o # nape, K a w e 3m H o M e p a u K ~ K
OHM y n o p n n o Y e H b 1 M e w co6oii.
Ta~ana B m H o M H o c T a RsnreTcr, no cyruemy, n p o r B n e H u e M c~oiicmaM a p K o B o m npouecca,
K c r r o p o e B sanaqax y n o p n n o s e H n n snpeqae-rcx B e c b M a penKO.
BbLnOnHJleTcJi HeKOTOpOe
H e 0 6 ~ 0 p l i ~ b IYCJIOBUX
X
neo6xonw~oey c n o B H e
OnTUMiUlbHOCTU.
- B cna60k U c H J I ~ H o@
~ ~o ~ M ~ x . )
C y m e m o ~ m u exom
661
omoii n o n y m ~ o ln
HeB03MOKHO ~ ~ C K O H ~YMeHbIIIeHHe
~ H O ~
(K~UVUBI~~pa3
40-U.n y C T b M
( H m e 6ynm ~ a m e ma
~o
e p e m o B m
-
o6ecnequsae~crTeM, rn
H a KOHeSHYm B C ~ H ~ H H3 H
~ a)' i e H H I
e C T b MHOXeCTBO BCeX nOllyCTHMbD( IIepeCTaHOBOK. 3 H W U e H ~ O ~ X O P H M O I Y )
ycno~uxo n T w m . n b H o c r w
03~a.rae-r,YTO M H o x e m o M H e mnmo n e p e c e K a e T c n c
f l u e UenUKOM C O n e p X H T er0. cJlefl~BaT&lIbH~,
~n eop ie ci r a H o B K u B M e m p a c c M o T p e H u r scero M H o x e m a
n e p e m o B m
MHOXeCTBOM OIlTUMaJlbHblX IlePeCTaHOBOK, HO
npu
HaxoweHuu
o r n u ~ a ~ ~ b
M.
P =(s,,s,, . . . ,s, ), o ~ e B w , H o , ~ e o 6 x o m ~nonya
nto6oii ee r a m pfi)= (s,,s,, . . . ,s,) (i = I :rn-I), T.e. B b l n o n H e H H e ~eo6-
nepeCTaHOBOK MOXHO O f p a H U W i T b C l PaCCMoTpeHUeM TOJlbKO MHOXeCTBa
XO~~CTUMOC
n e~ p e m o s m
CTUMOCT~
u m~
pa3MepOB.
3 0 CBO~~CTBO,B n O J l H e a H a J l O r H Y H O e I l p U H r u l n y
n p o r p a M M u p o B a H u x , H ~ O ~ B O J I Xn ~o cTT e n e H H o CTPOMT~n e p e B o
OllTHMaJlbHOCTH nHHaMHYeCKOr0
scex n o n y m u M b l x
nepecmoBoK,
K;1K YaCTHY HbIX, T a K U nOJIHb1X.
Jlro6oW i-ii y p o s e H b 3mro n e p e B a C O O T B ~ T C T B ~ ~i-ii
T nnoruwtce, T.e. i-MY
M e c q B MCKO-MO~
(i = 0 : m). B samomu, ~yneaoiiy p o s e H b ( s e p m u ~ a )n e p e B a c o o T s e T m s y e T
~ y n e ~ onnoruawe,
ii
H a ~ o ~ o p opiai3 M e u a e T c a manosan (~yneaoiiCT~HOK). Ans y c T a H o s n e H u R
nepecraHoBKe
B03MOXHOCTH y)lJlMHeHM
TOW
MnM
WHOW
S~CTUYH
AO
O ~~Y~C T U M OI l~e p~e c T a H O B K U
( pa3BeTBneHWI
nepe~a)HCnOflb3yeTCX M a T p H u a A, K O T O p m CTPOHTCX, KaK yKa3aHO
OCHOBe M a T p H U b l ~ Y 3 O D O T O K O BQ : A = Q - Q' = 11 A k r I lat+l
( k Y = 0 : 111 ).
u ~ o cnpu
~ b y m u H e H u u n a ~ ~ o 'iI ~
i C T M ~ H O Gn e p e c m o s K u coxpawmcs m u H ~ TB
C O O T B ~ T C T B ~ ~ U ye 3~nOa
Bblme, H a
A o n y c ~
3aBHCHMOCTU
OT
BbInOJlHeHUR
H ~ O ~ X O A U M O ~YCJTOBM
O
OIlTHManbHOCTU
rn
Y)~J~MH~HHo~~
s a c r ~ r ~ o ni eip e c r a H o B K u . 3r0 ~ O ~ B O J I R nmym
~T
nonymmym s a m u q y m n e p e c T a H o B K y ,
c o o T s e T c r s e H H o , nu60 Y,MUHUT~ ( ~ . epa3su~b
.
C O O T B ~ T C T B ~ysen
~ ~ Unepe~a),
~ ~
nu60 O T ~ P O C M T ~
KaK H e n e p c n e K T u B H y m .
A n r o p u ~n o~c q o e H u x M C K O M O ~ On e p e B a o n u r u e M no u r n y m u no m w H e ( i ) 'iacmq~ofi
n e p e m o s w ( PO) ):
a) n o c T p o e H u e y s n o ~nepsozo (i = I) YPOBHR n e p e B a ( ~ . e p. a 3 s e ~ ~ n e ~
B eup e
r u u H b t nepe~a):3 ~ n
Y3.rlbl M M e m T B C e Te H O M e p a
'
r;
rn KOToPblX
BblIlOflHXmTCX (KIK
y c n o ~ A,
~ : 2 0 ( I 5 r 5 m);
6) u ~ d y ~ r n u s ~doqnye~ue
oe
- n o n y c T u M , STO yxe n o c T p o e H a
c r a t i o e l t a PO) = (s,, s,, . . . s,) (I Ii I111-1) H, C n e n o B a T e n b H o ,
.
Ha
CfleAyeT H 3 Y T B e p W e H M
1)
nepeH M e e M C O O T B ~ T C T B ~ I Q U H ~ysen
norrycTuMm qacTurHan
i-My p o B H e n e p e B a .
TO 0 3 H a q a e T B b l n O f l H e H H e ~ e o 6 x o ~ o yCnOBUA
ro
ronb~oiin o w a T p u u b 1 :
B) u ~ d y ~ m u s ~ bnepexod
l i i
-K
npUCOeflHHMTb C n p a B a CneAJQOUUe
O ~ T H M ~ J l b H O C T U,l&JlA
_
cne.LIJ'I€l~efiTpey-
u~emrueiicaT p e y r o n b ~ o i in o n M a T p u u e 6 y ~ e Mn o c n e n o B a T e n b H o
c r o n 6 u b l C HOMepaMH S : ( A
, A , , . . . , A,,, )' (S f
,
f S, ,S 2 , . . . , S;), IlPOBePIlll K-lfi
pa3 B b l n O n H e H M e H ~ O ~ X O ~ U MYCJlOBuR
OI'O
OnTMMaJlbHOLXM
p.nn pacruupe~~oi3
T p e y r o n b ~ o i in o B M a T p u w 1 . Te H o M e p a s, m KOTOP~IX C o o T B e T c T B y m u a n
pacmupeHHan TpeyronbHm
nowaquua
ynoBneTBopxeT H ~ O ~ X O ~ U M O
ycnoaum
M~
onTuManb-
(i + 1)-MY p O B H e
nepesa H e p a 3 B u B a e T c n , T.e.
HOCTU ( ~ c A u , p a 3 Y M e e T C a , T a K O B b l e OKZX)'TCR),U O ~ ~ ~ ~ Y
y3JlbI
I O H
Ta
nepeBa.
B n p m B H o M cnysae p a c c ~ a T p u s a e ~ by3en
~ i i H a i -M
OH oKa-
ypoBHe
3blBaeTCR lyDHKOBbIM.
0 6 p a 3 0 ~M H O X e C T B O B C e X n O n Y C T H M b I X ( ~ o J I H ~ I x ) I l e p e C T a H O B O K
kf),Bbl'IHCJlAeM AJlA K a ~ 0 f Hi 3 HHX 3 H a S e H H e 40-U.
Te H 3 HHX, JUlB KOTOPbIX
~ O C T P O H B TaKHM
(MHO-X~CTBO
3T0
3Ha-SeHHe
I l O ~ M H O X e C T B eM
96
IlBnlleTCX
,T a K
MUHHMUIbHbIM,
U
IIBIIRmTCR
OIlTHMUIbHbIMH
H H a M H O X e C T B e BCeX ~ ~ ~ ~ C T ~ H O BEcnu
O K ) M. H O X e C T B O
(KIK
M
Ha
COCTOHT
U3 ~ A U H C T B ~ H HnOe p~e~C T a H O B K H , T O
~ e o 6 x o n u ~ oYCJlOBHe
e
OnTUMZLIlbHOCTH IlepeCTaHOBKki
OKa3blBaeTCR, e C T e C T B e H H 0 , H AOCTa-TOYHbIM.
Ecnu
0n~0fiK
O T K ~ ~ ~ TOT
~ Cn Xo q o e H m B c e r o M H o x e m a
M, a O r p a H u q u n c R
noqoeHueM
numb
~ K O ~ ~ - M
I l e~pO
e c T a H O B K U H 3 3 T O r 0 MHOXCCTBI, TO O H a M O X e T 6 b l ~ bB3RTa B KaYeCTBe XO-
p O l l l e r 0 n p H 6 J I l l m e ~ ~ 0 r P0e U e H l l l l . n p H 3TOM, eCTeCTBeHH0, O H a H e 0 6 1 1 3 a T e n b ~ 0RBJlXeTCR OnTU~ N l b ~ ~T.e.
f i O
, H a M O X m OKa3aTbCX JlUUlb O K O J ~ O O ~ T U M Z L I ~ ~ H O ~ ~ .
Peure~uesadavu c nomovaw o d u ~ o v ~ anepe~ocos
rx
Onpedene~ue.O n u ~ o q ~ bn erp ~
e H o c o M B nepecraHoBKe Ha3oseM nepeMerueHne B ~ei2
o f l ~ o n ,~ a ~ o r o - n u 6
H0
o M e p a c 3 a ~ u h f a e ~ o HM
r o M e m H a npyroe M e m o .
O A U H O ' I Hn ~e pI e~H~o c B n e p e m H o B K e O A H O ~ H ~ ' I H Oonpenenxmcx M H o x e m B o M S B c e x T ~ X
HOMepOB, 'IeP3 K O T o p O e OH OCYueCTBJlReTCR. %O MHOXeCTBO HenOCpeACTBeHHO CJleJlYeT UnH
I l p e n l l l e C T B y e T n e p e H O C H M O M y H O M e p y COOTBeTcI.seHH0 er0 I l e p e H O C y B n p a B O W l H BneBO.
O n u e o s ~ b ~n eep e H o c b 1 M O ~ KO ~ ~ C C H @ H U H ~ OHBa~6Tn~u n c ~ t i e( ~ . e H. a c o c e n H e e M~CTO) u
d a n b ~ u (e ~ . en. e p e M e u e H u e 6onee YeM H a o n H o M~CTO), a Tame snpaeo H 6neeo. taw^ 06pa30~,
n o n y q a e T c R r m b r p e ux B w a .
1. B e n s s n ~ aU 3 M e H e H U R 3 H a Y e H H R Ll[@-U ( n p H OnHHO.1HblX l l e p e H 0 c a x )
6 n m w f i n e p e H O C B n p a B O K~KO~O-nu60
HOMepa O Y e B w H O PaBHOCllneH 6 n w e ~ y
nepeeocy B n e B o C o c e n H e r o c HUM c n p a B a H o M e p a . h 6 o f i u3 3m n ~ y xn e p e H o c o B RBJIX~TCX 3 n e ~ e ~ TapHbrM n p e o 6 p a 3 0 ~ a ~ a
nea~~ ~ on iei p e m o B m . n o ~ ~ coo o ~T s eyT c T B y m r u y m B e n u r a H y u s ~ e H e H m 3 H a ' I e H u R 4 0 - H MOHCHO H a x O n H T b , n O n b 3 y J l C b Y T B e p W e H H e M
1. A e f i C T ~ H T e n b ~ o3TO
, yT-
6 n m u f i n e p e H o c HoMepa k BnpaBo
m u , B c e ~ ~ B H'ITOO H o M e p a r B n e s o , B n e Y e T u s ~ e ~ e s~~ua es e ~ 4u 0x - u H a ~ e n u v w ~Ab
y .
T ~ K H06pa30~,
M
npu n e p e M e u e H u u H a o n ~ M
o e m ~ a ~ o r o - n u 6H0o M e p a B n p a B o ( ~ o ~ k)e p
B e p m e H s e M O ~ cO@ o p ~ y n u p o ~ a
Hm
B cnepym~ue~
Bme:
UJIU BneBO ( H O M ~r)~ COOTBeTcTBy~llQ'H,
BeJlHYHHy U 3 M e H e H M 3Ha'IeHUX 4 0 - H
(Ab)
CJleJlYeT
6 p a ~ bB M a T p H U e A p H 3 CIPOKU UJIH c~on6uaC T e M Xe HOMePOM (H3 CTPOKU k H n H m n 6 u a r).
M ~ o r o ~ p a n~p ~u Moe eH e H u e y T s e p W e H w x 1 n o 3 ~ o n ~0m
6 0 6 r u u ~ bero, T.e. nonyqun cne)lyIOLUUe ma cnedcmsurr, y K a 3 b l B m u H e BenHYHHbI H3MeHeHUX 3 H a ' I e H M 4 0 - H H n p H nal'lbHUX
nepeeocax.
1. n p n n a n b H e M n e p e H o c e B n p a B o (B n e p e c T a H o B K e P ) ~ a ~ o r o - n u 6H 0o M e p a k, T.e. npw nepexone
OT n e p e m o m u P = ( . . . ,k, S , . . . ) K n e p e m s o B K e (. . . ,S, k , . . . ), U ~ M ~ H ~3 ~Ha ~He ~ w - 1
40-u COCTaBnaeT B e n U ' I U H y 1s E A (CYMMY COOTBeTCTBYlOuHX 3JleMeHTOB k-# CTPOKU
2. npw n a n b H e M nepewoce B n e B o (B n e p e m o m e P ) ~a~oro-nu60
H o M e p a r, T.e. npa nepexone
OT n e p e m o s u P = ( . . . ,S, r , . . . ) K n e p e c r a e o B l t e (. . . , r , S, . . . ), H ~ M ~ H ~s H
~ aH ~~ e ~ u n
U@-H
COCTaBnReT BeJlH'IHH)'
C s E sA,
(CYMMY COOTBeTCTBYtOIIlUX 3 n e M e H T O B T-TO C T O J I ~ U ~
MaTPHUbl AP ).
flefiCTBHTWlb~0,
nmb~kifi n e p e H O C
HOMepa
MOHCHO
IlOCJIenOBaTeJlbHOrO n p U M e H e H M HeCKOnbKUX 3 n e M e H T a p H b l X
IlepeCTaHOBOK, T.e.
6nwux
PaCCMaTpUBaTb
KaK
pe3yJlbTaT
npeo6pa30~a~wfi
IIOJly'IaFOLUUXCR
IlepeHOCOB 3 T O r 0 H O M ~ P ~COOTBeTCTBeHHO,
,
B n p a B O UJIH BJIeBO.
B b l n o J I ~ e ~ HKe m O r O H 3 3TUX
COOTBeTCTBylOl4+e BeJIH'IHHbI BU)la
npeo6pa3o~awwi2IlpHBOAUT K H3MeHeHkllO 3Ha'IeHHX q@-u
Ha
A k, H 3 k-fi q O K U W l H B m a L\ sr H 3 r-r0 cron6ua ~ e p X H e f i
UQ-H, cornacno cnenmluo
1,
Ha senesnHy
Z>:;.r+lA~ k
k -1
Ci=r
AS.s
r k
i
20
Z;l'k+l Asks,
) m u nepen ~nanosoii( r a ~ o l
(r=t+~:m, t = ~ : m - ~ )
(r =O: k-2, k = 2 :m).
20
,&fiCTB~~enb~o, ~ e 0 6 ~ 0 , l l U M b l M
y c n o B w e M OlTTHManbHOCIM n e p e c m i o B m i P, OYeBU.5H0, IBnmmn H ~ B O ~ M O X C H O Cee
T ~ynyqrueann 3a C Y ~ T~a~oro-nu60
O ~ H O Y H O I - On e p e H o c a . 30
sep6anbHO c @ o p ~ y n w p o ~ my~
c nooeB n e H p a B H o c m b H o , K ~ K
cneAyeT B p e y n b ~ a ~
n pew m e q e H n n cnenCTBBA 1 H 2 (CM. Bblllle), aHaJWiTUqeCKU c @ o P M ~ J ~ H P o B ~ H H ~YCnOBHIM
~M
(4), T.e. HeOTPWUZtTeJlbHOCTU BCeX Y W a H H b I X B (4) YaCTUClHbIX CYMM '(C)'MMC IlePeMeHHblM BepXHwM M H HUXHWM ripeAeJlOM CYMMHPOBSLHWR).
Q ~ M ~ T U M' I, T 0 IlOCKOnbKy B YCnOBHH
(4)
(a
HepaBeHCTB AOcraToYHO MHOrO
HMeHHO
m2
IIITYK), TO 3TO yCnOBUe n m a e T c r J l O ~ q H O xecmm, T.e. ~ J I U ~ K U M
K H ~ O ~ X O A U M O M YH
n o c ~ a ~ o s ycnosw
~ o ~ y o r r r u ~ a n b H o mnepemoami. C n e n o s a ~ e n b ~ M
o ,H o x e m B o M n u m b He
H ~ M H O ~mnpe
O
M H o x e c r s a B c e x o n m M a n b H b I x n e p e m o B o K . Ann KWO#
n e p e m o s m ws
M H o x e m a M BO~MOIKHOCIM ee y n y q r u e H w n 3a c r e ~
O A U H O ~ H ~ I Xn e p e H o c O B w c q e p n i u b l H,
Cne.IlOBaTeJlbH0, BCe OHW RBIUIKYrCI ( ( ~ 0 ~ 0 3 P U T e J I b H b l M H )H) a OllTHManbHOCTb.
OTM~TWM, ClTO H ~ O ~ X O ~ W MYCJlOBHeM
~IM
OllTUManbHOCTU IlepeCTaHOBKU
B u n o n H e H w e CnenymLUwx H e p a B e H m
Xy=,.AOs, 5 0
P
XBJlneTCH TaKme
(r=2:m ) , & , A S j S m5 0 (r = 0 :m-2 ),
03HaYaK)lUHX HenOnOXU'IWlbHOCTb YKa3aHHbIX SaCTUClHbIX C)'MM 3neMeHTOB n e p B 0 l CrPOKU W
nocnemero c m 6 u a M a T p e u b l A,.
Ann n o K a 3 a T e n b c r s a m r o B O
~ ~ Mn3~ (2)
M ypaBHeHnx
m
npn k = 0 w k = m :
r-1
o = Z ~ = ~ =A Zj=lAosj
~ ~ ,
+ Z y = r A m j (rk2:m).
(cornac~oy T s e p m e H w i o 2), TO
w3
mix
y p a B ~ e ~ w af in o n y q n M
cnpmennweom
noKa3blsaeruwc
HepaBeHcrB.
YTsepmne~we2 M O ~ cO @ o p ~ y n w p o ~ aH~ Bb B u A e o6pmom y-mepmeann: e m rn
~a~oZi-nu60
nepemoami xmn 6 b 1 owa u3 ~ M BM@ o p M y n a x (4) n m n m q w u m b ~ o f iTO
,
3 ~ na e p e m o B K a H e nmamn o r n ~ a n b ~ o if lie.i i C T B k i T e n b ~ 0 , m n e p e m H o B K a M O X ~ T 6 b m
ynywuewa H a ~ e n n ~ w
MOA~JUI
~ y moii C Y M M ~ In y T e M c o m e m x B y m m e m o m H o w o r o n e p e H o c a B
H ~ A .Ecnw k e C T b HOMep q 0 K U (c~on6ua),B KOTOPO~~HaXOnUTCI 3Ta oTpkiUaTeJlbHM CyMMa B
98
K ~ KB U m O , B 3TO# IIOAMaTPHUe UMeeTCR OTpU4iYTeJlbHaR CyMMa, P a B H m (-91,
pacnonoxeman B m n 6 u e 4 ( o ~ 06sene~a
a
~ P R M O ~ ~ O ~ ~ H H KC
On
Me) n
. o ~ a ~ e n bn~e o
p e, M e c T u B B
IlepeCTaHOBKe P C O O T B ~ T C T B ~ I O H
~O
UM
~ e~p 3 BneBO, a UMeHHO n O C T a S U B er0 nepen HOMePOM 2
(~.e.C p a 3 y I l O C n e KJ'I~.~~oBo#), n 0 n y l r R M yJ'IyqllIeHHyf0 I l e p e C T a H O B K y P' = (3, 2, 1, 4, 6, 5) CO
s ~ a l r e ~ 44)-u
u e ~
F(P3 = F(P) - 9 = 1332 - 9 = 1323. J I e r ~ onposepm, STO n e p e c T a H o s K a P'
yxe H e y n y r w a e M a c IIOMOUILK) OLU.~HOYH~D(
nepeaocos, T.e. n n X H e e s b m o n m m x y c n o B r n (4),
H Il03TOMY O H a XBIUIeTCA I l 0 ~ 0 3 ~ k i ~ W l b H 0 H
f i a OnTHMaJ'IbHOCTb. O ~ H ~ KKaK
O , 6 y n e ~n O K a 3 a H O
H M e , OHa H e R W e T C I oIITuM~JI~Ho~~.
3. Haxoxaenue orrru~anbnoiinepecranosm
H a i i n e H H o e sbme H ~ O ~ X O . ~ U ycnoaee
MO~
O~TUM~~~HOC
nepemaosicu
TU
( ~ e p a s e ~ c (4))
na
IlOnOXUM B OCHOBY O n U C a H H O r O B b l l l l e a J l r O p u T M a BeTBJleHUR. B pe3ynbTaTe kl I'IOJlyYHM BCe
MHOXeCTBO HCKOMbIX O n T U M N I b H b l X K P Y r O B b M PaCCTaHOBOK CTaHKOB.
n p u ~ e p3.
rpy30nOTOKOB
nepeB0
UCXOnHbIX AaHHbIX
JUlR
n0nyqeHUR
U3 IlpUMepa
MHOXeCTBa
M
1
U
HafineHHofi
B HeM
( M H O X ~ C T B ~ BCeX
MZiTpUUbI
nOl'I~~MblX
n e p e m a o ~ o ~n )o ,c r p o e H H o e no O ~ U C ~ H H O MsYb l w e a n m p u - r M y B m n e H r n , n o K a 3 a H o H a PHC. 1.
npounnlocrpupye~K a ~ o f i - n U 6 0 war anropema, H a n p u M e p pa3sume yzna (3, 2, 4) H a
T p e T b e M Y p O B H e n e p e B a ( ~ u c I),
. T.e. y3na, KOTOPOMY COOTBeTCTBYeT H a 3 H a ' f e H U e CKUIKOB 3,2,4
H a n e p s b l e TPU nnoua~m.n p o 6 y e ~n o o r e p e n H o H a 3 H a q a T b H a C n e p y m u y m ( ~ ~ T B ~ w K ) )
IlJIO~anK)' OCTaJIbHble CKUIKU 1,5,6.
,&M ~rr01-0,
BO-nep~b~x,
K c o o ~ s e T c r B y m q e i iq e y r o n b ~ o f ni o n M a T p u q e A,,
nooqepeneo
coomeTmymuue ~ J I ~ M ~ H-T Hynesble
~ I
(q,,= q,, = 0) , a Torna, cornacHo yTsepxneHuro 1,
nonyraeTcR u Hynesoe npwpaueHue
3~aqe~m
U@-u (A = A = 0) npe J I I O ~ O M
ynopnnoseHue 3 ~ 0 knapbr cocemux ~ K O B .
A H ~ J I o ~ u CnpaBennuBo
~HO~
nnn ~ K O 1Bu 6 BO B T O P O ~u TpeTbefi nepecTslHoBKax.
,Quqemeprofi nepecTaHoBm ~ o n u s e m oBUTKOB no BceM m u npemeTaM passo,
COOTBeTCTBeHHO, 2, 3, 3, 3, 2, W O AaeT 3HaqeHUe U@-u - 1298, KoTOpOe MeHbIIle, YeM Nil TpeX
UepBblx nepeClXHOBOK. CJlenoBa~eJIbH0,OHa RBJlXeTCn ~ , Q H H ~ T ~ ~ 0IlTU~aJlb~0fi
HHo~~
IlepeCTaHOB~oii.n e p ~ b ~
x e ~ p u3
u y ~ a 3 m ~ bqeTblpex
w
nepecTaHoeoK r m m c s OKonoornManbHblMu, HO
ynyruu-rb ux MOMO nuub c noMowm TpynnoBoro nepeHoca ( o m i o s p e ~ e ~ ~ onepeHoca
ro
HeCKOJlbKwx HOM~POB).
,
,
Pewenue sadauu c no,wou(bw deofinbrnnepenocoe
Onpedene~ue.A B O ~ ~ HnepeHocoM
~IM
B nepemoslce HmoBeM nepeMeueHne B ~ e i myx
i
KWX-nu60HOMePOB C 3aHUMaeMblX UMU MeCT Ha JlPYrlie MecTa.
B03b~eM~ a t c y ~ o - J I HnepecTaHoBKy
~O
(HOMCPOB
C T S I H KPOUBnap)'
)
HOMePOB k U r B ~ e f iHe
.
orpaHwqusan O ~ U H O
MOMO
~ , C S U ~ T ~TO
, k 4 r ( 4 C U M B O ~n p e m e m o ~ m m )u Torna k
M O T e T 6bITb U HyJIeM, T.e. K n a 0 ~ 0 f i .P ~ C C M O T~a~oiZ-nu60
~UM
UX Dofi~ofinepeHoc.
&m onucmm p ~ o i i ~ o nepeHoca
ro
paccnnolpullr B nepecTaHosKe P He nycme MHoxecrsa
S, H S , ,onpenemmuwe, coomercTseHHo, onuHosHble nepeHocb1 HoMepoB k u r B 3mfi nepeCTaHOBKe (KaK 3T0 6b1~10CMaHO BbIWe
OnUCaHUR OAUHOSHOM) nepeH0ca) U, CneAOBaTeJlbHO,
He ysmbremuue nepeHoc npyrom e3 HoMepoB 3mii napbl ( ~ . e H
. e sasucnruwe OT mro, ecTb OH
unu ~ m )M
. o m 0 C S U T ~ T ~wo
,
~awwljiu3 rnwx O ~ ~ H O S H ~nepeHocoB
DL
B crrpblse m npyroro u3 ~ u He
x uenecoo6pme~,T.e. npe nepeHoce HoMepa k, HanpuMep, BnpaBo, a HoMepa r,
HaIlpUMep, BJleBO BblnOJIHRHYrCR (coI'JI~cHoYCJlOBHllM (4)), COOTBeTCTBeHHO, CJIeAyIOruwe
HepaseHma:
-
(5)
'3m
(...,...,..., r, ) ,
P Or ,
(..,...,...,...,
)
0
, ( , , k, . '7
r,., .
I I
(...A-..J
,..., ..., ...).&
o K W c n nepeHeceHHb1Mu 06a HoMepa, He c o s n a m c S, u S,, T.e. n u MHoxema
,4B0kHbU nepeHOCOB,
COOTBeTCTByIOl4iX
YKa3ZIHHblX
kl
OXapaKlZPH30BaHHblX
H ~ O ~ X O J ~ U M ~kiI X nOCTaTOqHblX
OAHHOYH~IM nepeHocaM B
C MqKki
3peHkir BbInOnHeHHR
AJIH HUX
~ c J ' I o B u ~ ~ Hen>meCmeHHOCTki
AByM
c o o ~ ~ e ~ ~ ~ ~ y rrmnb r pue ux cmn6uax
x
~ a 6 n3.
.
Ta6nuya 3. Xapamepumum AonycruMwx nsoiinblx nepenocos Bcex verwpex BWOB
I
Bum
3
I
4
Hmsawue
llepe~oc BHYTP~ UH- llepe~oc 3a uHTepean n e p e ~ o cHoMepoB k u r llepe~ocHoMepoa k u r
TepBana (k, r) (u Torna [k , r] (u Torna HoMepa snpmo (a, cnenoea- Bneeo ( u cnenoeaHoMepa k u r nepeao- k u r, KaK H LUIR Bma 1, TenbHo, HoMepa k u r T ~ J ~ ~ H HoMepa
O,
k u r
cmcn B pa3~bieC T O ~ H ~ I , nepenocnTcn B pmHue nepeHocnxn B o m o ~ nepeaocnxn B OAHOM
cropom,
Hmcrpeqy ~ a n p a a n e w ) c cox- ~ a n p m n e w ) c coxHmcrpelty npyrnpyry).
panemehi ux n o p w a p a ~ e ~ uuxe ~nopma
DPYr ~ P Y V ) .
(k 4 I.).
(k 4 r).
h o 6 p a x e ~ u Be nepemoBKe P
1
'-3
.,. ..,. ...r,. ..)
(...,k,..
i
2
(...,...,k\L
,...,r ,...,...)
1
I
Heo6xomoe U ~ O C T a T O q HYWIOBUe
~
HeToXCQeCTBeHHOCTUJlByMOPllHOqHblM IIepeHOCaM
Memy HOMepaU k U r M ~ o x e s r s o SI CO- MHoxemo S1 c+ MHOX~-0 S2 EOuMenar
MeHbmeR nepnarr XOTH 6~ uienepm, x m
cne- n e p m r x m 6b1 n p
Mepe ma HoMepa.
nymmfi 3a r H O M ~ P , a wmuuii 3a r HoMep U, ~ ~ n y u uLUIR
i i k HoMep
MwoxeCTBa
S2
He
MHOXeCTBO S 2 Eo- qoMe TOM, B myqae, U, KpOMe TWO, B
~
B c hWoxen
~nepmT ~ XO6~ Korna HoMepa k u r CnYqae, Korna HoMepa k
CTBOM
BCeX HOMepOB npemnymHfi
k ~ J U I ~ ~I ~I c e m mu u U r IIBJIXmTCA CO~emn(y~ o ~ e p ka u~r uu, HoMep.
C e W H W HOMeP r
~ o ~ ke ne-pe~ocu~cn
p
P M e TOrO, B cJrY- 3 ~ - ,
HOMep ~TmuTcfl nePen nPeq m HoMepa k 3a mew-to@
k HOqae S 1
S 2 =A (A - u r MOrnu 6blm H nocne r, TO nocne WPYW
nepe~oca~ o ~ e rp m
ai MePM, TO nome Henycroe MHOX~CTBO),
~.e. c o c e ~ .
i
~ o ~ e pk aH r yxe ~e P ~ H O C H~ O M ~ Pk~ m
~ o r n a ~ o ~ e pka u r
~OJIXWI
6 u ~ bcocen- HoMepa k H r Yxe He
OKa3blBaIOTCR c 0 c e ~ AOJW-IM
6 ~ cocan
HUMH (maye B TOM
MU, ( ( p a ~ m m nomy
)
n
nocneme~
cnyqae HHMU ( ~ ~ a qB e 3 ~
TY x e napy H O M ~ ~ B ,
cnyqae
J ~ B O ~ ~ H O R nepeHOc nocnemeM
((BKRMHBaK)TCII)) B Om0
i
papamocunes
same a ~ o i i ~ o inepeHoc
H
TO
xe
~ecro,
Awe onO ~ O M Y O ~ H O ~ H O M YBHOCmeH
sbmonunemn
ycnoBue
OWHOwOMY
nepe~ocy ~ n e ~mor o HoMY
k > r ( - C H M B O ~cneBnPmo m1-0
~ o ~ e pqepes
a , ~ o ~ o p nePeHocY
~ k
nowm).
n e p e ~ e c e ~napa
a
k, r). HoMePa. qePe3 KO3 m m , TO B cnyqae
mpuii nepeHeceHa napa
S 1 S 2 f A ycno~uek
k . r).
>r BblnOJIHneTCX amMamqecm.
'
'
n
0
~
+
n
1. B e n u v ~ ~
H3MeHeHUZI
a
3HBYeHHII 4 @ U (npki ~ 0 f i ~ Ibl e Up e H O c a ~ ) .
3~a~u
BenkiqnHbl
e
U~M~H~HU
3 I~I a q e ~40-H
m npu O D U H O ' ~ H ~ I nepeHocax
X
B nepecraeoBKe
(CM. BMllle CIIeACTBkiI 1 ki 2) n03BOnXeT 06061l(ki~b 3TOT pe3ynbT;rr U Ha c J I ~ W~ ~B O ~ H ~
nepeeocoB. C o o ~ s ~ y r o u kaopMynb1
ie
pacqeTa LUIX Bcex paccMa.rpnsaeMbuc YeTblpex BUAOB
n ~ o i i ~ onepeHoca
n,
n p k i s e n e H b r B ~ a 6 n4. B ee crpo~ax2 H 8 ( @ o p M y n b ~(6H8)).
102
I X
A H ~ J ~ H T H ~ ~ cBKb O
l p a~ X e H H e :
(6)
ZAh+Ab+XAsr
s 4
sd2
seS,,s#r
scS2,s#k
r p a @ H q e c K o e ~ 3 0 6 p a X e H H (B
e MaTpHUe
...k I@, +I
...
...
r
Ap):
... k K-S,
...
-1
\
r
r
I
Heo6xow~oeYCJlOBHe OTPHUaTeJlbHOCTH
<O
IlpHparrleHWI:
~ s e ~ , , s i r< A
O . ~
~ s e ~ ~ , Asr
s + < kO
~ ~ J ~ H T H Y ~ BcbK
lpO
M e~H H e :
Z s.S,,sirA
b +Xreq
(*)
1 ZSES,
Ah
+
r p a @ H Y e c ~ o e~ 3 0 6 p M e ~ H
(BeM Z I p H U e
... k K,-
S, >
-,I
Xses2,s*k A ,
... k . . . .
...
f
5
\
&
r . . .
f
\
r
(t--S2*
Heo6xow~oeYCJlOBHe
*kr'
L
OTpHJ&lTeJlbHOcrH
Z s E ~ l , s # I A k <t O
-
.oL
r
Ah'o3
(9)
Ap):
J
npHpUeHHR:
C s E S 2 , S # k A s r <'
npyrOr0 B
nm6oii
(C
TO'tKU
3 P H U H KOHeqHOm
p e 3 y J l b ~ a ~ a n) O W e n 0 B a T W b H O C T U :
IlepeHOC
P ) H o M e p a k u 3 m (B
~ n o n y q w g r u e f i c a H ~ M ~ H ~ Hn H
e pOe ~m ~o s K e P')
r unu n e p e H o c (B ucxon~oiin e p e c T a H o B K e P ) H o M e p a r u 3 m ~
(B nony.rasrueiicrr
H ~ Hn H
e pOe ~m ~o a K e P" ) H o M e p a k. C n e n o s m b ~ o senurmia
,
u 3 ~ e ~ 3e ~wa q e ~ uu@-a
n B
(B H C X O ~ H On~e~p e m o m e
HoMepa
H ~ M ~
pe3YJlbTaTe
~ B O ~ ~ H OnN
e p)e H O C a
MOXeT
6blTb
H m e H a
n e f i ~ ~ B U T e J l b H 0C
n o c n e n o s a m b H o r o n p u M e H e H u n cnencr~uii1 u 2 (CM. ~ b ~ r u e ) .
B 3~0iix e ~ a 6 n u u en p u s e n e H o u r e o M e T p u q e c K o e mo6paxe~ueB e n u q u a
COOTBeTCTByto4Ue
3 n e M e H T b I B e p ~ ~ e fT pi e y I W l b H o f i
2. Heo6xoamoe YCJlOBHe OlWHMaJIbHOCTH IlepeCTaHOBlu!
Y m 6 e p ~ d e ~ 3.
u eH e o 6 x o n u ~ b YCJlOBHeM
l ~
OnTMMaJlbHOCTH
nonHeHue
senusuH
A,,
I l O ~ a T p U m IMaTpUllbl
nepeCTaHOBKU
1
,'
nOMO4bH)
(6H9) - I
06Bene~b1
P HBIUIflCR Bbl-
m ~ ~ ~ M ~ Hsepx~eii
T O B T p e y r o n b ~ o i in o n M a T p u s b r M a T p u u b r Ap H e o T p u s a T e n b H o c T u
suns (6)-(9) m B C ~ B O ~ M O H ~ I Xn o n y c r u M b o < ~ B O ~ n~e pIe HXo c o B B 3-roii nepe-
CTaHOBKe.
A ~ ~ C T B U T ~ J ~H~ ~H OO ~, X O ~ U MYCJlOBUeM
~IM
OllTUMZUlbHOCTU IIepeCTaHOBKU
~ ~ R ~ T CH H~ B O ~ M O X H O C ee
T~ ynyltrueHm
P,
O q e B W H O , HB-
3a crm ~a~oro-nu60
n ~ o i i ~ onreop e H o c a . 30e e p 6 a n b n o
c 4 o p ~ y n u p o s w ~ oycnosue
e
u p a B H o c u n b H o , KaK cnenym B p e 3 y n b ~ a ~n pe a a n e q e H u x + o p ~ y n
(6)-(9) (CM. ~ a 6 n4. ), aHZUIUTU1leCKH C@OPMYJIWPOB~HH~~M
B Y T B e P m e H U H 3 YCJIOBUHM.
YTBepXJleHUe 3 M O H O C ~ O P M ~ J I U P O B U
~ TB~ B W e O ~ ~ ~ T HY TOB ~
e PO
m e H U X : e C n H JIJM Ka~0fi-nu60IlepeCTaHOBlu! X O T H 6 b l O A H a U 3 CYMM BUAa (6)-(9) HBJlReTCR 0 T p ~ I J a T e n b H 0 f i (COOTB~Tc T B y l O 4 U e H ~ O ~ X O ~ UYCJIOBUH,
M ~ I ~
06nemamuue nOUCK OTpUuaTeJlbHblX CYMM, C Y W T O M
H e p a B e H c T B suna (5) y ~ a 3 a ~ b
B 1q 0 K a . x 6 u 12 ~ a 6 n .4), TO 3 ~ nae p e c T a H o B K a H e x m m
0nTUMaJlbH0fi. A e f i ~ ~ B t i ~ e J I b H
3'l'a
0 , n e p e C T a H O B K a M O X e T 6 b l ~ bYJTyqlUeHa H a B e n H q H H Y MOL(YNI
3mii
C Y M M ~ In y T e M c o o m e T C T B y I o u e r o
nsoii~oron e p e H o c a
B
~ e f iH
. o ~ e p a(k u r) c r p o ~unu
CTOJI~UOB, C O O T B e T C T B y t o ~ U e3~0fiO T ~ U U ~ T ~ J I CYMMe
~ H O ~ B~ TpeyI'onbHofi
IlOnMaTpUIJe MaTpUUbl
Ap , RBJIRIOTCR n e p e H o c u M b l M u (npu x e n m u y n y ' ~ r u u ~ nb e p e m ~ o s q )B n p a B o (sneso)
c o c r r e e ~ c ~ ~ y rM
o ~eeme H o M e p a M u B n e p e c T a H o B K e P.
n p u ~ e n nep~u M e p b r
B
~ B O ~ ~ nHe ~p eIHXo c o B B c e x s m b l p e x B U ~ O B ~
, J I Y ~ I I I ~ E OTY
U UUJIU
X UHYIO
u c x o n H y m nepecraHoBKy.
li'pawep 4. &m UCXOAHMX n a H H b m u3 n p u M e p a 1 p a c c M o T p u M me cnenymuue nepemros( n e p U~3 ~HUX M O X e T 6 b m YJTyYllleHa, KaK nOKa3aHO B n p U M e p e 2, U C lIOMOlJJbt0 OnUHOqHOro nepe~oca):(2, l , 4 , 3 , 6 , 5 ) , (3,2,4, I, 6,5). n o ~ a x eYTO
~ , OHU H e R B J I R ~ T CO~I I T U M ~ ~ ~ H ~ I M U .
Coo~semmymruueXUM n e p e m w o B K a M T p e y r o n b H b i e n o n M a T p u m r (c yrmoni M a T p u u b l
~ ~ ~ ~ O ~ O T OnKo O
c rBp,o e ~ ~ oB #n p u M e p e 1) u M e w cnenymuuii sun:
KH
~ O ~ ~ I T HK ~U T UB 3TUX IlOLIMaTPUUaX OTPUUaTeJlbHble
YClleUHbIMU
3TUX
-
CYMMbI BUAa
(6x9)
XBnRKlTCX
COOTBeTCTBYlOUUe 3 n e M e H T b I 3TUX n O P M a T P U U 0 6 ~ e ~ e ~IlPXMOYrOJIbHUKaMU.
b l
CYMM
nOKa3blBaeT,
9TO
B
PaCCMaTpUBaeMblX
IlepeCTWOBKaX
uenecoo6pa3~0
OCYUleCTBUTb, COOTBeTCTBeHHO, C n e . Q W W U e ~ ~ 0 f i H b nleep e H O C b l (OHU n O K m a H b 1 C T P ~ ~ K ~ M U ) :
B p e 3 y J l b T a T e I~oJ'I)'~uM,
COOTBeTCTBeHHO, C J l e ~ I O U U e YnJ'qLUeHHble
(3,6,2, 1,5,4) ,
3 ~ a l r e H ~ ~X Q - u
N R HUX
(3,6,2,1,5,4) , (4,3,6,2,1,5) ,
IlePeCTaHOBKU:
(3,6,2, 1,5,4)
MeHbLUe, 9 e M N X U C X O ~ H b l XIlepeCTaHOBOK H a MOnyJlU 0 6 ~ e n e H ~ b l x
I l p X M O y r O ~ b H U K a M UCYMM, T.e. COOTBeTCTBeHHO H a
34,25,25,25.
3. H a x o m e ~ u eo m u ~ a n a ~ onepemaHostcw
ii
H a h e ~ ~ b Bl beI l u e ~ e 0 6 ~ 0 n k i ~ by Cl Jel 0 B U e OlYTUMaJlbHOCTU IlepecTaHOBKU (CM. Y T B e P w e HHX2 U
3) n O n O X U M
B OCHOBY OllUCaHHOrO
Xe BbIUIe
W l r O p U T M a BeTBneHUX.
B pe3ynbTaTe
IlOJly-
SUM BCe MHOXeCTBO UCKOMblX O l l T U M U b H b l X KPYrOBbIX PaCCTaHOBOK CTLWKOB.
McnonbsosaHue
6onee X e c T K o r o
H ~ O ~ X O A M M Oy~ cOn o ~ m(6onee M e n K o r o
cum, ynysmes-
HOrO O U J l b ~ p a )Qrul nOCTpOeHMIt y3JIOB A e p e B a ( C O ~ ~ ~ CKOTOPOMY
HO
H e U e J l e c 0 0 6 p l i 3 ~ b l H e TOnbKO
OAUHO'iHbIe, HO U A B O ~ ~ H
n e~
p eIH~O C b l B COOTBeTcTBymUUX ClaCTM'IHbIX I l e p e C T a H o ~ ~ a Xn)p U B 0 -
nm- K TOMY,
TO H e K o T o p b I e B ~ B Un e p e B a o T c e K a m T c r r
( y ~ o p a s u ~ a m ~ cBap)e, 3 y n b ~ a ~rero
e
OHO
~ H O B U T C XM e H e e ~ ~ C T ~ I M .
n p t ~ ~ 5.
ep
KOB n e p e B o
CTpOeHHOe
ms
no
UCXOAHbIX AaHHbIX U 3 I l p U M e p a
nonyseHun MHoxecTsa
1U
H ~ @ ~ H H BO H~e M MaTPUUbI rpy3Onon>-
M ( ~ ~ o x e c mB cae x
nonycruMblx
n e p e m ~ o ~ ono~),
2. B p e 3 y J l b T a T e
OIlUCaHHOMY BbILUe aJ'IrOPUTMy BeTBneHHR, nOKil3aHO H a PUC.
M COCTOUT U 3 ~ ~ u H C T B ~ H H aO IIOTOMY
~~,
U o I ~ T u M ~ J ~ ~ HIlepeCTaHOBo~~,
(3,6,2, l,5,4).
npounnmcrpupye~~ a ~ o t i - n u 6mar
0 3~01-o
anropu-ma, H a n p u M e p pmeume y3na (3,2,4,1)
H a qeTBepTOM Y p O B H e n e p e B a ( ~ u c2).
. n p U PaCCMOTpeHUU TOJlbKO OnUHO'IHblX IlepeHOCOB 3TOT
y3W XBJIXJlCX, KaK n O K a 3 a H O B l l p U M e p e 3, IlepCneKTHBHblM, u60 6 b m o B03MOXHO er0 pa3BUTkie
(XOTR u ~ P N H C T B ~ H H O~ )ysen (3, 2, 4, 1, 6) (CM. p ~ c 1).
. M c n o n b s o ~ a ~ xe
u e ewe u n ~ o i i
n e p e H o c o B m c e K a e T , KaK BWHO u3 n p u M e p a 4, T a K y m B O ~ M O X H O C T ~T.e.
,
A e n a e T y3en (3,2,4, 1)
TyllUKOBbIM, H e I l 0 , I U e X a U U M Pa3BUTUH), H e IlepCIIeKTUBHblM (CM. PUC. 2).
A ~ a J ' I o r l l ' i ~ on p o s e p n e T c x o T c e r e H u e u eue T p e x y m o ~
( y ~ o p o s e ~ ~emefi)
ue
(3,2, 1,4, 6),
(3,2,4,6), (3,6,2,5) n e p e B a H a p u c y H K e I. B p e 3 y n b ~ a m
~ ei x Y e T b I p e x o ~ c e s e ~ uuf nonysami
cx n e p e B o H a puc. 2.
nOJlyqUM, 'IT0 MHOXeCTBO
KU
~ b ~ ~
' r o n o e a B.r. ~ K O H O M H ' I ~ C KBO~POCM
H~
nnannpoeui 060pynom~~a
B C B ~ ~c ~~~Befiepnxuuiefi
H
npo~3~0~1cr~
~ M ~ T H KBH~ K O H O M
n.,
UK
1965.
~ . Bun.3. C.134-145; H e R M a p K A.M., r o n o B a B.r. 3 n e ~ e ~ r 1 . 1
paC'IeTa o I I T H M ~ ~ H WIWHpoBKH
o~~
p a 6 0 . 1 ~M~ W Ha IlUlYl'IHofi nHHHH // M~T~M~THKo-~KoHoMH'I~cKH~
npo6nehcsl.
Jl..1966.Bwn.58. C.166-176; P o M a H o B c K n R M.B. 3ana~ao ~aneslron~eRlueR
~pyroeotipaccraHosKe ~ H K O BI/
~ K O H O M H KH ~MmeM. MeTonsl. M.. 1%6. T.2. Bun. 4. C. 578-581; H e ii M a p K A.M., illeii H Ma H P.ll., r on o B a B.r.
Pacrm H nporpawqmnanne ~ ~ C ~ H O B060py~omna
K H
B uexax. M.,1969; K n H M o B A.H.. 0 n e H e B M.A.,
C o K o n H u sl H C.A. O p m w n a H nnannpoeanne npo~3eoncreaHa ~unnocrpomnbnoM3amae. n.. 1973. kin.2.
C. 60-61; 1979. M.
3. C. 62-63; C M T H H K B.@.. K a p a r o n o e a E.A. MaTe~m'IecuieMonenn e m a n ~ p o w
H ~ ~
ynpaen,eHHH I'IpeNlpHSTHXMH.KHeB, 1985. C.101-104.
- P 0 M a H 0 B C K H fi M.B. fbIr0p~~hIbl
pellleHHI 3KCrpeManbHbuc3aa'I. M.,1977.C. 225227.
P o M a H o B c K H R M.B. 1) A n r o p m ~pemenna
~
srcrpe~anbebuc3ana.l. C. 248-251; 2) mc~pemwRilHaJlH3.
Cll6.. 2000. C.195.
'T lo T IO K H H B.K. Onepameno-~anennap~oe
nnannpomne Ha n e p e ~ e ~ ~ o - n r n 'nnnnnx
~ ~ s r xc nepexommn
sanenam N B m . ne~nnrp.YH-m.Jl..1991. BunA. C.54-61.
W y r x m e n n e o 6 o c ~ o e u m eyltruatlsoe
~
eulue npasnno nocrpoenna ~ a r p ~ l~30nOTOKOB
w
Q = 11 q b (1
(pacc~orpe~ne
ma KWOR napw craHKoa rex npenueroe. B TexnonomqecKnx Mapurpyrax K-WX
mi crattm
ximama C M ~ ~ MnM3a~eu
H , Haxoxnenue CYMMU BecoB Ha npoqmmsl m i x npen~moe).Y npymx m p o s no
npaBHn0 HHYeM He ~ ~ ~ C H OH,BCnenOBaTenbHO,
~HO
H B M f X C I nHlllb YMaHHblM Ha HlfIyHTHBHOM YPOBHe.
H e R M a p K A.M., r o n o B a B.T.3 n e ~ e m
pac~emo m ~ a n b ~ onnannpoeKn
ii
pa60q~xM ~ C THa nmqnoti
nnnnn.
I1 llpnuenenne M
'
'
Документ
Категория
Без категории
Просмотров
33
Размер файла
15 457 Кб
Теги
оптимальное, станком, поточной, расстановка, круговая, производства
1/--страниц
Пожаловаться на содержимое документа