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38120041JOURNALOFXIANJIAOTONGUNIVERSITYVol.381Jan.2004,(,710049,):.,,,,.,.:;;;:TP39117:A:02532987X(2004)0120064204ToolPathGenerationfor42AxisNumericalControlMachiningofArbitrarySurfaceBladesWuBaohai,WangShangjin(SchoolofEnergyandPowerEngineering,XianJiaotongUniversity,Xian710049,China)Abstract:Aneffectivemachiningmethodwasproposedformachiningarbitrarysurfacebladesusing42axisnu2mericalcontrol(NC)machines.Forspindle2tiltingtype42axisNCmachines,thefunctionalrelationbetweentheinclinationangleandtiltanglewasestablishedtoensurethatthetoolaxisisparalleltotheswingplaneduringtheentiremachiningprocess.Aflat2endcutterwasused,itspathsweregeneratedbasedontheconstantscallopheightprincipleandmachiningstripswereenlargedbyadjustinginclinationangle.Themethodimprovedthecuttingefficiencyof42axismachiningandenabledtotransferthetoolpathplanningmethodsof52axismachiningto42axismachining.Keywords:numericalcontrolmachining;arbitrarysurfaceblade;toolpath;constantscallopheight,,.,[13].,,[4][5],.,[6].,,,,0[6].,.,.,LL,.,.,,:2003204228.:(1975),,;(),,,.:(20020698042).'1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved..11[2].{OM;XM,YM,ZM};{Ot;Xt,Yt,Zt};{C;XL,YL,ZL},C,XL,YLC,ZL=XLYL.,ZLL(),YLL(),LL.,,,LL,.{OM;XM,YM,ZM,B},,YM.{OM;XM,YM,ZM}OMC,{C;X,Y,Z}.XCZ,Y0.2,{C;i,j,k}{C;i,j,k}{C;X,Y,Z}{C;XL,YL,ZL},M.i=a11i+a21j+a31kj=a12i+a22j+a32k12k=a13i+a23j+a33kM{C;i,j,k}{C;i,j,k}(x,y,z)(x,y,z),[7],x=a11x+a21y+a13zy=a21x+a22y+a23zz=a31x+a32y+a33z(1){C;XL,YL,ZL}T0=(0,1,0),ZLLYLLM1=cosLsinL0-sinLcosL0001M2=cosL0-sinL010sinL0cosL,{C;XL,YL,ZL}T=T0M1M2=(-sinLcosL,cosL,sinLsinL),{C;X,Y,Z},Yy=0,(1)y=-a21sinLcosL+a22cosL+a23sinLsinL=0cos=a21/(a221+a223)-,sin=a23/(a221+a223)-,L=arccos[a22cotL/(a221+a223)-]-(2),LL,.22.1,,,.[1]d=8hkeff,/2k/2-(3):keff,/2k/2;h.,C+,-.k/2keff,/2.561,:©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.C,3.e1e2,XL,e2.ZXL.[8]X.3C,X[9]k0=kmaxsin2+kmincos2(4)k/2=kmaxcos2+kminsin2(5)k=kmaxsin2(-)+kmincos2(-)(6):kmaxkminC;k0k/2CXLXL.X,[8]keff,=sin2cos2sinr-k0+k0-cos(-)sincos(kmax-kmin)sin2(7)XL,=/2,keff,/2=1cos2sinr-k0+k0-tan(kmax-kmin)sin2(8)[8]keff,/2k/2.(3),,.,L.,,Lkeff,/2.(2)(8),L,,.2.2d,C(u,v).,RuRv0.[1,2],du=-dcos(RvXL)(RuXL)(RvZL)-(RuZL)(RvXL)(9)v=dcos(RuXL)(RuXL)(RvZL)-(RuZL)(RvXL)(10),C(u+u,v+v)..(1),.(2),(3),L;,(9)(10).(3),.(4)(2)(3),.3Ot,.Ot=C+COtCOt=LM1M2:L,,L=(-r,0,0);M1M2LL.Ot=[xC-rcosLcosL,yC-rsinL,zC+rcosLsinL](11):xCyCzCC.4.,,20mm,0.1mm,45.,45.5893.1mm.,20mm,8965.2mm.,34.3%,.,,6638©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2:LL,;LL,.545.,.,.:[1],,,.[J].,2003,37(1):7780.[2]LeeYS.Non2isoparametrictoolpathplanningbyma2chiningstripevaluationfor52axissculpturedsurfacema2chining[J].Computer2AidedDesign,1998,30:559570.[3]LoCC.Efficientcutter2pathplanningforfive2axissur2facemachiningwithaflat2endcutter[J].Computer2AidedDesign,1999,31:557566.[4]SuhSH,LeeKS.FouraxisCAMmoduleforNCma2chiningofrotational2freesurface[A].Proceedingsofthe1991IEEEInternationalConferenceonRoboticsandAu2tomation[C].Piscataway,NewJersey:IEEE,1991.13021308.[5],.[J].,2001,37(4):4447.[6]VickersGW,QuanKW,Ball2millsversusend2millsforcurvedsurfacemachining[J].JournalofEngineeringforIndustry,1989,111:2226.[7],,.[M].:,1984.4751.[8]RaoA,SarmaR.Onlocalgouginginfive2axissculpturedsurfacemachiningusingflat2endtools[J].Computer2AidedDesign,2000,32:409420.[9],.[M].:,2000.7379.(),(22),4,,20031019.,,,.761,:©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.