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22920109JournalofComputerAidedDesign&ComputerGraphicsVol.22No.9Sep.2010:2009-11-02;:2010-03-15.(1971),,,,;(1984),,,;(1981),,,,;(1972),,,,.陶佳安1),高胜林2),游清宁2),施群2)1)(200072)2)(200072)(janetao@shu.edu.cn):,,,S.,CAM,1.5~3.3.,NC,,,,.,.:;;;S:TG659LookaheadandAccelerationDecelerationAlgorithmsforMicroLineBlocksMachiningTaoJiaan1),GaoShenglin2),YouQingning2),andShiQun2)1)(SchoolofCommunicationandInformationEngineering,ShanghaiUniversity,Shanghai200072)2)(SchoolofMechatronicsandAutomation,ShanghaiUniversity,Shanghai200072)Abstract:Inmicrolineblocksmachiningwithrealtimecurvereconstruction,theoriginalcontourofworkpiecesusuallycannotbereconstructedaccurately,andthecontourerrorsofthereconstructedcurvesexceedstheallowablelimitofcontourerror.Curvereconstructionconditions,includingcornerangleconditionwhichdependsonallowablefeedrateofthecornerangle,chordlengthconditionwhichisbasedoncorrelatedchangeofthecorneranglesandchordlengthsofsuccessivemicrolineblocksaregiven.AfeedrateprofileplanningalgorithmacrosstheknotsofthereconstructedcurvewithSshapeaccelerationdeceleration(accdec)ispresentedinlookaheadandaccdecalgorithm.SimulationsandexperimentsusingthesenewmethodsshowthatthemaximumcontourerrorbetweenthereconstructedcurveandthemicrolinesislessthanthepermissiblecontourerrorsetinCAMsoftwareforsegmentingtheoriginalcurveintothemicrolineblocks,andthemachiningspeedis1.5~3.3timesthespeedoftraditionalmachiningprocess.Theresultsindicatethatbyusingthenewalgorithms,geometryelementsoforiginalcontourofworkpiecescanbedistinguishedfromNCcodeeffectively,andthebasepointscanbefound,sotheoriginalcontourofworkpiecescanbereconstructedaccurately,andtheinterpolationpointspasseveryknotofthereconstructedcurveprecisely.ThemethoddiscussedhasapplicationincomplexcontourmachininganddesigningmiddleorhighgradeCNC.Keywords:microlineblocksmachining;curvereconstruction;lookahead;Sshapeaccelerationdeceleration,.,,,[17],[23,6]S[1,5][8].,,,.[913](computernumericalcontrol,CNC),,,.,,,,;,,.Erkorkmaz[9],;,,.,;,,.[10],,,;,.,.Yau[1112][13],BzierB;CNC,,,,,.[1113],,,.,,,;S...1,,,.,,.,,,.,,(NC,),.1.11.1.1ABB15719,:vB,aB,BC,,1.Vmax,T,amax,Jmax,,[6]vBT!amax2sin(2)aBT!Jmax2sin(2)(1)vB=vmax,aB=amax,v=2arcsinT!amax2!vmax,a=2arcsinT!Jmax2!amax,=min{va};amaxJmax,.=0~(2).,2G01.11.1.2,,,.2,,L=2tan(2),-=(1-cos).,(),.CAM,,,i-1=i=i+1=,Lii,LiLi-1=2tan(i2)2tan(i-12)=tan(i-12)tan(i2)(3)Ki=tan(i-12)tan(i2),,K.LiLi-1Ki(4)2CAM(2,i+1i+1),,.,(3)Li+1Li=tan(i2)tan(2).(2),tan(2)tan(2),Li+1Li∀tan(i2)tan(2)(5)(4)(5),tan(i-12)tan(2)LiLi-1tan(i-12)tan(i2)(6)(),.(6).(6),iG01,,.(2)(6),.157222MG01,,1.1,A,B,C,D,E(2)(6),ABG01,AB,G01BC,CD,DE.1.20~,.,(1).2S,,S,,.2.1i,Hermite(HermiteNURBS,CADCAM,,CNC),u.uiui+1,,P(ui)=Pu(i),P(ui+1)=Pu(i+1),P!(ui)=P!u(i),P!(ui+1)=P!u(i+1),P(u)=[1u-ui(u-ui)2(u-ui)3]!10000010-3!2i3!2i-2!i-1!i2!3i-2!3i1!2i1!2iPu(i)Pu(i+1)P!u(i)P!u(i+1)(7),uiuui+1,!i=ui+1-ui.t=t(u)=u-ui!i,(7)[0,1]P(t)=P(t(u))=1tt2t310000010-33-2-12-211Pt(0)Pt(1)P!t(0)P!t(1)(8)P(t)u,P!u=dPdu=dPdt!dtdu=1!i!dPdt=1!iP!t,P#u=1!3iP#t.u=uiu=ui+1,P!u(i)=dP(t(ui))du=1!i!P!t(0),P!u(i+1)=dP(t(ui+1))du=1!i!P!t(1).,P!t(0)=!i!P!u(i),P!t(1)=!i!P!u(i+1).Pt(0)=Pu(i),Pt(1)=Pu(i+1);(8)P(t)=[1tt2t3]10000010-33-2-12-211Pu(i)Pu(i+1)!iP!u(i)!iP!u(i+1)(9)P(t)=Pu(i)+!iP!u(i)t+[3Pu(i+1)-3Pu(i)-2!iP!u(i)-!iP!u(i+1)]t2+[2Pu(i)-2Pu(i+1)+!iP!u(i)+!iP!u(i+1)]t3(10)S,,,P#t=d3Ptdt3=,P#u=1!3iP#t,Jt=!3iJu=!3iJ,J,J,J=|J|.(10)P#t=d3Ptdt3=2Pu(i)-2Pu(i+1)+!iP!u(i)+!iP!u(i+1)=!3iJ,P!u(i+1)=!2iJ-P!u(i)-2!i[Pu(i)-Pu(i+1)];[Pu(i+1)-Pu(i)]!i=!P^i,!P^i.P!u(i+1)=!2iJ-P!u(i)+2!P^i,vi=P!u(i),vi=P!u(i+1)=!2iJ-P!u(i)+2!P^i(11)15739,:(11)i(vi=vi-1),,S.,(9),.2.2CNC(9),Hermit,,.(9)P(t+!t)=V+U0(t)+U1(t)+U2(t)(12),V=Pu(i);U0(t)=W0∃t,U1(t)=W1∃t2,U2(t)=W2∃t3;U0(t+!t)=2∃U0(t)-U0(t-!t),U1(t+!t)=2∃U1(t)-U1(t-!t)+U11,U2(t+!t)=2∃U2(t)-U2(t-!t)+U22;U11(t)=2∃W1∃!t2,U22(t)=6∃W2∃!t2∃t;W0=!i!P!u(i),W1=[-33-2-1]Pu(i)Pu(i+1)!iP!u(i)!iP!u(i+1)=-3∃Pu(i)+3∃Pu(i+1)-2∃!iP!u(i)-!iP!u(i+1),W2=2-211Pu(i)Pu(i+1)!iP!u(i)!iP!u(i+1)=2∃Pu(i)-2∃Pu(i+1)+!iP!u(i)+!iP!u(i+1).CNC,(2)(6),SJ;(11),(9),(12).33.1NCCNC,CNCG01,.G,NCISO6983.3.3CNC,CADCAMNC.NC,,SG01.3.2.MasterCAM,0.025mm,4.4MasterCAM157422,.CAM84G01,5G01,I,II2G01(%!&),,2.5G016,%.&,G01.6,,,.6G01,7(8),S,G010,,15.880s,3970.,9.G01,;S,0,,6.152s,1531,.CNC,,.CAM,,15759,:,.,,,0,10,%*&.10S,38.741%,.,S,,19.344%.,0.02492325mm.NC0.025mm,10E4,.11type4,,,11.:J=50000mms3,Vmax=150mms,T=0.004s,Vs=0mms,Ve=0mms.12NCG01.12NCG0113,,,.1314()14,15762248.144s,15,28.924s,60.078%.,,,.155:1),,,.2),,,,.3)S.,S,,.4),,1.5~3.3.,,.(References):[1]CuiJ,ChuZY.AnimprovedapproachfortheaccelerationanddecelerationofindustrialrobotsandCNCmachinetools[C]ProceedingsofIEEEInternationalConferenceonIndustrialTechnology,HongKong,2005:12691273[2]YePeiqing,ZhaoShenliang.Studyoncontrolalgorithmformicrolinecontinuousinterpolation[J].ChinaMechanicalEngineering,2004,15(15):13541356(inChinese)(,.[J].,2004,15(15):13541356)[3]XuZhiming,FengZhengjin,WangYongsheng,etal.Highspeedadaptativelookaheadinterpolationalgorithmforcontinuousmicropathsections[J].ManufacturingTechnology&MachineTool,2003(12):202