多色集合的研究及在机械产品概念设计中应用-李宗斌

14720027JOURNALOFCOMPUTER-AIDEDDESIGN&COMPUTERGRAPHICSVol.14,No.7July,2002李宗斌1)　赵丽萍1)　凌永祥2)　李天石3)1)(710049)2)(710049)3)(710049),,.,;,;.,,,TH391StudyofPolychromaticSetsandItsApplicationintheConceptDesignforMechanicalProductsLiZongbin1)ZhaoLiping1)LingYongxiang2)LiTianshi3)1)(StateKeyLaboratoryofManufacturingSystemEngineering,XianJiaotongUniversity,Xian710049)2)(FacultyofScience,XianJiaotongUniversity,Xian710049)3)(CollegeofMechanicalEngineering,XianJiaotongUniversity,Xian710049)AbstractFuzzymathematicsmodelbuiltuponthebasisofpolychromaticsetsisdevelopedtomodelingandanalyzingthediscretesystem.Designrulesandsearchalgorithmareworkedoutforconceptualdesignofmechanicalproducts.Thesearchalgorithmisabletofindoutseveralfeasibleschemesofproductdesignconformingtotheestablishedtechnicalspecifications,resultinginasetofcandidatesolutions.Evaluationfunctionsareappliedtochoosethemostreasonableone.Anexampleofmachiningcenterlayoutispresentedtoillustratethefeasibilityofnewapproach.Keywordspolychromaticsets,contour,complexobjectandsystem,fuzzymathematicsmodel:2001-06-04;:2001-09-14.(59885005).,,1946,,,.,,1963,,,.,,1946,,,.,,1946,,,,.1:(1),,.()..(2),().,;.(3),.,,.,,.2.Pavlov1988[1],1995[2],2000[3].,(),,.,,.,.,.,.,.,.,.,,.,,[4].,,,.,.2.1PSPG,(contour)..[2-3],.,;.,,:(1),;(2),;(3)();(4).,.,.,,,..2.2aiûLA~(ai)A~,LA~(ai)aiA~.A2,aiA,LA~(ai)=0.,A~A2aiA~L(A~)[5-6]A~=A2=(a1,a2,,an)L(A~)=(LA~(a1),LA~(a2),,LA~(an))PaiA2(ai\LA~(ai))(1)A~AAA2PaiA2(aiA,$-i(A)LA~(ai)$+i(A))(2),$-i(A)AaiLA~(ai),$+i(A).,$-i,$+iA,A,,An,F~FF2PFiF2(FiF,$-i(F)LF~(Fi)$+i(F))(3)(1)(2)(3),,.,(3),FiFFi(F)=1,$-i(F)LF~(Fi)$+i(F);0,.[A$F(A)]F~(A)[ALF~(A)],[AF(A)][AF~(A)][AF~(A)]=[AF(A)],[A$F(A)],[ALF~(A)][A$F(A)]=$F1$F2$Fm($-1(1),$+1(1))($-1(2),$+1(2))($-1(m),$+1(m))($-2(1),$+2(1))($-2(2),$+2(2))($-2(m),$+2(m))($-n(1),$+n(1)($-n(2),$+n(2))($-n(m),$+n(m))a1a2an[ALF~(A)]=LF~(F1)LF~(F2)LF~(Fm)L1(1)L1(2)L1(m)L2(1)L2(2)L2(m)Ln(1)Ln(2)Ln(m)a1a2an2.3.,,.,U(S),S.,pi,pjS6897:F(pi),F(pj).,SF(pi),F(pj),F(pi)F(pj).U(S)U(pi,pj)=1-ASF(pi),F(pj)(4)U(pi,pj)=1-AS2F(pi),F(pj)(5)UÊ(pi,pj)=11+AS2F(pi),F(pj)(6)pkPU(pk,P)=1nni=1U(pk,pi).nP.U(F(pi),F(pj))pipj.,(4)(6).U(S)=1-S100(7)U(S)=1-S21002(8)U(S)=11+S21002(9)1n=100,(4)A=1n,(5),(6)A=1n2(7)(9).1(4).(5)S,S,.,U(F(pi),F(pj)),1,F(pi)F(pj).33.1F(pk)Pipk.,,:(1)G=(P,C)Li[3],4;(2)F(A)k=F(A)áF(pk)(10)Lipk.,LiPi,.(10)F(A)áA,,.F(A)F(A)=F1F2Fn=nj=1Fj,F(A).,(10)F(A)k=F(A)á=F(A)áF(pk),,Fi(pk)=1Fi(A)á=1,pk.F(pk)F(A)á1.,.U(F(pk),F(A)á)1,pk,(10).,.3.2G=(P,C)Li,.,.PG,,.,.Li=(ai1,ai2,,ain).F(Li)A,F(Li)A=R(F(ai1),F(ai2),,F(ain))(11),,Li=(ci1(i2),ci2(i3),,cin-1(in)).F(Li)C,F(Li)C=R(F(ci1(i2)),F(ci2(i3)),,F(cin-1(in)))(12)PG,F(Li)(11),(12)F(Li)=R(F(Li)A,F(Li)C).3.3CAD,.F(Li)A=nk=1F(aik)(13)F(Li)C=n-1k=1F(cik(ik+1))(14)Li,F(Li)=F(Li)AF(Li)C(15)AaiA,F(Li)=F(Li)A(16)Paik-1,aik(F(ak)=F(aik)\F(aik-1)Á).aiF(Li)6902002,.F(A)F(C),.Paik,aik(k+1)Li(F(aik)F(cik(ik+1))=F(aik))(17)vaik,aik(k+1)Li(F(aik)F(cik(ik+1))F(aik)).(17),F(Li),,.F=(F1,F2,,Fn),PF(A),F(C)(F(A),F(C)AF),F(Ai),F(aik),F(cik(ik+1)),.,(13)(15)F(Li)A=nk=1F(aik),F(Li)C=n-1k=1F(cik(ik+1)),F(Li)=F(Li)AF(Li)C.3.4,F(Li)A=nk=1F(aik)(18)F(Li)C=n-1k=1F(cik(ik+1))(19)F(Li)=F(Li)AF(Li)C(20)(16),(17),Pcik(ik+1)Li(F(cik(ik+1))=F(aik))(21)aik.(17)(21),F(Li)=F(Li)A.,(18)(20)F(Li)A=nk=1F(aik),F(Li)C=n-1k=1F(cik(ik+1)),F(Li)=F(Li)AF(Li)C.4[7],.:Step1.,.N.Step2.Q=qi,.Step3.,M=c(q1,q2).19([8]1519,.15,,19.,).WQ=wk.,Step2Step3.q1,q2Q,wkqk.113(),579,2,4,6,8ij,ji.NStep4.Step1N7,Step5.Step7.Step5.Step2,U(U={Uk},Uk=uk(Si,Sj):i,jN,qkQ).Step6.Ak=ak,akqkSi.AkA=Ak,Si,..Step8.Step7.,A(A=aik:iN,qkQ).9.Step6.Step8.O(O=AW).Step9.,.5,:Step1.F(pk)F(A)á$-U(F(pk),F(A)á)1,1.Step2.G=(P,C)Li.Step3.Sn.a.F(A)k=F(A)áF-(pk)F(A)á,pk,S;b.nF(A)á.Step4.LipkU(F(pk),F(A)á).,(4)F(pk)F(A)á.Step5.pkF(A)á.U(F(pk),F(A)á)$-U(F(pk),F(A)á),pk,pkPi;.6917:LiF(A)á,LiPi,.,.Step6.,.62,.,.,[9].7(1),.(2).,:.,,.pkP,1..(3).[1]PavlovVV.Polychromaticgraphofmathematicssimulationfortechnicalsystem[A].In:ProceedingsofScientificandTechnicalConferenceCAD-88,Plovdiv,Bulgaria,1988.810(inRussian)(‘±³½À³ƒƒ.‘À½ºÇÂÀ¾±ÄºÉ¶Ã¼º¶´Â±Æͺ¾Àµ¶½ºÂÀ³±¿º¶Ä¶Ç¿ºÉ¶Ã¼ºÇúÃĶ¾³“‘’[A].³ÄÀ¾±Äº¹±ÈºÑ¼À¿ÃÄÂźÂÀ³±¿ºÑºÁÂÀ¶¼ÄºÂÀ³±¿ºÑĶǿÀ½À´ºÉ¶Ã¼ºÇÁÂÀȶÃÃÀ³.±ÅÉ¿À-ĶǿºÉ¶Ã¼±Ñ¼À¿Æ¶Â¶¿ÈºÑ“‘’-88,’¶¹Ð¾¶µÀ¼½±µÀ³,‘½À³µº³,‚À½´±ÂºÑ,1988.810)[2]PavlovVV.Mathematicssimulationofdiscreteproductionsystem[J].InformationTechnology,1995,(0):1519(inRussian)(‘±³½À³ƒƒ.¾±Ä¶¾±ÄºÉ¶Ã¼À¾¾Àµ¶½ºÂÀ³±¿ººµºÃ¼Â¶Ä¿À´ÀÁÂÀº¹³ÀµÃij±[J].Š¿ÆÀ¾±ÈºÀ¿¿Í¶Ä¶Ç¿À½À´ººº,1995,(0):1519)[3]PavlovVV.PolychromaticSetsandGraphsforCALStechnology[M].Moscow:STANKINPress,2000(inRussian)(‘±³½À³ƒƒ.‘À½ºÇÂÀ¾±ÄºÉ¶Ã¼º¶¾¿À¸¶Ãij±º´Â±ÆͳCALS-ĶǿÀ½À´ºÑÇ[M].Ž:“”ŒŠ,2000)[4]OsetrovVG.Propositioncalculustodetermineassemblysequencesofmachine[J].JournalofMachineBuilding,1998,(3):2933(inRussian)(Ã¶ÄÂÀ³ƒ„.ŠÃɺý¶¿º¶³Íü±¹Í³±¿º»ÁºÁÂÀ¶¼ÄºÂÀ³±¿ººÁÂÀȶÃÃÀ³Ã²À¼º¾±Êº¿[J].ƒ¶ÃÄ¿º¼¾±Êº¿ÀÃÄÂÀ¶¿ºÑ,1998,(3):2933)[5]HeXingui.FuzzyTheoriesandFuzzyTechniquesinKnowledgeProcessing[M].Beijing:NationalDefenceIndustryPress,1998(inChinese)(.[M].:,1998)[6]LiHongxing,WangPeizhuang.FuzzyMathem