correctedcornerradius

Chapter9.
FiveAxisToolPathGenerationMethodsOptimizedNC-toolpathgenerationfor5-axismachiningofcomplexsurfacesProf.
Dr.
Ir.
I-P.
Kruth(Jean-Pierre.
Kruth@mech.
kuleuven.
ac.
be)KatholiekeUniversiteitLeuven,Celestijnenlaan300B,3001Heverlee,BelgiumProf.
Dr.
Ir.
B.
Lauwers,IrP.
DejongheandIr.
1.
DotremontKatholiekeUniversiteitLeuven,Celestijnenlaan300B,3001Heverlee,BelgiumKeywords:CAD/cAM,5-axismillingAbstract:Thetoolpathgenerationmethoddescribedinthispaperisenhancingthesculpturedsurfacemachiningmethods,whichcanbefoundincommercialCAM-softwarepackages.
Toolaxisinclinationoptimizationisdonebasedonthepropertiesoftheunderlyingsurfaceandisaguaranteeforgouge-freeNC-toolpaths.
Thetoolinclinationvariesalongthetoolpathinsuchawaythattoolinclinationisoptimizedforeachindividualtoolposition.
TheproposedmethodusesprojecteddrivepatternsandisabletotakecareofmUltipleandeventrimmedpartsurfaces.
1.
INTRODUCTIONFiveaxismachiningoffreeformsurfaceshasmanyadvantagesifcylindricalortoricalcuttersareusedinsteadofballnosecutters.
Comparedtotraditionalthreeaxismachining,thematerialremovalrateincreasesandthemachiningtimereduces.
CommercialCAM-systemswithmulti-axiscapabilityareforcingtheoperatortogivethetoolacertainconstantleadand/ortiltangle(1)withrespecttothesurfacenormal.
Furtherasetofmultipleandtrimmedsurfacescanbemachinedwithinoneoperationthroughtheuseofdrivesurfaces.
Thedrivesurfaceisusedtogeneratetrajectoriesinacontactdrivenway,whicharethenprojectedontothepartsurfaces.
Thetoolorientationiscalculatedbasedeitheronthedrivesurfaceorthepartsurface.
Smallleadanglesarefavourabletothematerialremovalrate,surfaceroughnessandsurfaceaccuracy[2].
But,applyingasmallconstantleadanglealongthemillingpathcancausedifferentproblemslikegougingandvariationsinthescallopheight.
Asasolutionforthis,severalresearchershaveinvestigatedthedynamicoptimizationandadaptationofthetoolinclinationalongthetooltrajectory[1][2].
Themaindrawbackofmostofthesemethodsisthattheyarecontactdriven.
Thismeansthatthetoolisguidedalongtheisoparametriclinesofthepartsurface.
Asaresult,onlysinglesurfaceswithouttrimmingscanbemachined.
Thetoolpathgenerationmethoddescribedinthispaperoptimizesthetoolinclinationineachpointofthepartsurface.
ThesedevelopmentsfitintheframeoftheOPTIMACHproject.
ThegoalsofthisEU-fundedprojectare:Createreliablecollision-anderror-freeNC-programsthroughanon-lineclosedloopsimulationsystem.
Enhancemillingstrategiesinordertoimprovetheachievedsurfacequalitythroughoptimizingthetoolanglew.
r.
t.
theworkpieceandthestep-over.
Theoriginalversionofthischapterwasrevised:Thecopyrightlinewasincorrect.
Thishasbeencorrected.
TheErratumtothischapterisavailableatDOI:IFIPInternationalFederationforInformationProcessing199910.
1007/978-0-387-35392-0_40G.
J.
Ollingetal.
(eds.
),MachiningImpossibleShapesDependingontheprerequIsItesposedbytheusedCAD/CAMsystem,twomainapproacheshavebeenfollowedduringthedevelopment.
Thefirstapproachisbasedontheprototypesoftware,whichhasbeendevelopedinthepastatthedivisionPMAoftheK.
U.
Leuven[2].
Thesecondapproachisamorepracticalsolution,takingawaythedisadvantagesfromthefirstone.
Inbothcases,theinclinationadjustmentisdoneduringthetoolpathgenerationstep(greycolouredblockonFigure1)andnotduringNC-simulation,NC-verificationoronthemachine.
'"Loadll,20-'IFedral,200GOlDx,Y,z,i,j,k,Col/sonme$$llgeIN1T20M6IN2G1X,.
Y.
.
Z.
.
B.
.
C.
.
F300\.
jFigure1.
Overviewofthetoolpathgenerationprocessfora5-axisNC-program2.
FIRSTAPPROACH:NUMERICALOPTIMIZATIONBASEDONTHEANALYTICREPRESENTATIONOFTHEWORKPIECEGEOMETRY.
Forthisfirstapproach,thestandardCAD/CAM-routinesareusedtocalculateeachtoolposture.
Atoolpostureisthecombinationoftoolposition(xyz)andtoolorientation(ijk).
ThetoolinclinationascalculatedbytheCAD/CAM-systemisthenusedasthestartingvaluefortheoptimizationalgorithms.
TheroutinesofthestandardCAD/CAM-systemaregeneratingthetoolposturesinthefollowingmanner(Figure2):,A"".
.
/i)////.
/,///'//gJPSFigure2.
Methodforgeneratingtoolpostures344osAcertaininclinationangleisappliedtothetoolW.
r.
t.
thesurfacenormalofthecorrespondingtooltippointinthepartsurface.
Thetoolisthenprojectedontothepartsurface,whereacontactpoint(CP)isfound.
lftheinclinationangleappliedtothetoolislargeenough,thecontactpointwilllieinfrontofthecutter.
Theoptimizationalgorithm,explainedhereforacylindricalcutter,calculatesthemaximalangleoverwhichthecuttermayberotatedaroundthecontactpoint(CP)tofitascloseaspossibletothepartsurface.
Todothis,thealgorithmconstructsafunction8=f(u,v)representingtherelationshipbetweentheunderlyingsurfaceofthetoolandtheangleoverwhichthecutterisallowedtorotate.
ThisfunctionisthenminimizedtoobtaintheangleTheminimizationprocedureisbasedonatwo-dimensionalNewton-Raphsonmethodstartingfromagivenpointonthepartsurface.
Theresultofthisminimizationmethodisthenearestlocaloptimuminthesurroundingofthegivenpoint.
Figure3.
ElementarydiscinsidethecutterThesizeoftheunderlyingsurfaceforwhichthefunction8=f(u,v)isdefined,isdirectlyrelatedtothetooldiameter.
Thechanceforhavingmorelocalminimaincreaseswiththesizeofthecutter.
Asaconsequence,theanglehastobecalculatedformorethanonepoint,tobesuretofindthesmallestone.
Thisisdonebychoosinganumberofpointsonthebottomofthecylindricalcutter.
Foreachpoint,thefollowingisexecuted:1)Computetheshortestdistancetotheunderlyingpartsurface.
Consequently,thenearestpoint(PI)onthepartsurfaceisfound.
2)Theminimizationisof8=f(u,v)isdonestartingfromthepointPI.
3)Repeatstep2untiltherequestedaccuracyisachieved.
s:;pCPworlDCP_.
.
_.
.
_.
.
_.
.
_.
.
-··'1Z··_.
.
-,:/.
/OSPSThefulltoolwiththeestimatedtoolaxisisprojecteddownonthesurface.
ThisisdonebyusingthestandardCAD/CAMsystems'functionalityfortoolprojection.
Thetoolprojectionreturnsacontactpoint(UCP),whichmightactuallybeinglocatedeverywhereonthebottomofthecutter.
Thetoolaxisisthenac(justed(acertainvalueisaddedforB),basedontherelationshipbetweenthecontactpoint(CP)andthecontactpointreturnedbythetoolprojectionmethodUCP.
TheoalistoetCPascloseasossibletoUCP.
347PSThetoolisprojectedagainwiththenewlyfoundtoolaxis.
Doingthetoolprojectioneverytime,gougingisavoided.
Stepse,0andf)arerepeateduntilacertaincriterionisfulfilled.
Possiblecriterionsare,'UCPcloseenouhtoCP,iJ.
8notositiveanmore,.
.
.
Ingeneral,after2or3iterationstheoptimizedtoolpostureisfound.
Greatcareistakentonotrushthetoolaxisvariations.
Fastdecreasesofthetoolinclinationangle{)cancausethecuttertocutwithhisback.
Thisisnotfavourablefortoolsthatdonotcutwiththecentre(e.
g.
toricalcutters).
Quicklyincreasingthetoolinclinationontheotherhandcanhelpthecuttertoavoidgouging.
Asaresult,thedisturbanceofthetoolinclinationangle{)perdistanceunitislimitedtodifferentvaluesfordecreasingandincreasingtoolaxisinclinationvalues.
4.
\MACHININGRESULTSFortheexperimentalverificationoftheappliedmethod,aworkpiece(dimensions100x100mm)withaconcaveandconvexregion(Figure6)wasmilledoutofureolandaluminiumusingafive-axisMAHO600Cmillingmachine.
Duringtheexperiments,atoricalcutterwithadiameterof20mmandacornerradiusof4mmwasused.
Thenumberoftracksalwaysequalsto20.
ZCIYCFigure6.
Surfacewithconvexandconcaveregion348OneworkpiecewasmilledwiththestandardroutinesoftheCAD/CAM-system.
Forthistest,aminimalinclinationangleof9degreeshasbeenapplied.
Anotherworkpiecewasmilledusingtheoptimizedtoolaxisinclinationroutines.
Thescallopheightofthetwoworkpieceswasinvestigatedusinga3DcoordinatemeasuringmachineCOORD3equippedwithaWolf&Becklaser-scanningprobe.
Figure7showstherawscanningdata.
·202040608J100120·1·2·3Figure7.
Measuredprofileoftheworkpieceintheconvexregion.
Forthisspecificcase,thelargestbenefitoftheoptimizedmethodcomparedwiththestandardmethodwasfoundintheconvexregion.
Intheconcaveregionthecutterwillalwaysbeforcedtoalargertoolinclinationinordertopreventgouging.
5.
CONCLUSION&CONTINUATIONOFWORKTheproposedalgorithmshavebeenimplementedinsideacommercialCAD/CAMsystem.
Experimentsprovethealgorithmsfromthesecondapproachtoberobustandgeneralapplicable.
Sincetheoptimizationofthetoolpostureresultsinalargermaterialremovalrateandasmallerscallop,theneedforanaccuratestep-overcalculationalgorithmisoriginating.
ACKNOWLEDGEMENTSTheOPTIMACHprojectisbeingcarriedoutintheframeoftheIndustrialandMaterialsTechnologiesresearchandtechnologicaldevelopmentprogrammeoftheEuropeanCommunitywithafinancialECcontributionupto1.
923kECU.
MoreinformationaboutthisprojectcanbefoundontheOPTIMACH-webpages:APPENDIXDifferentangularsystemsareinusetodefinethetoolaxisinclination.
Themostpopularsystem,whichalsoisfoundinmostcommercialCAM-systemsisthelead-tiltsystem349(Figure8).
However,theinclination-screwsystemhasadvantagesinthewaythecalculationsaredone,butislessobviousfortheuseroftheCAM-system.
normalvectorZznormalvectortoolcenterpoint0toolcenterpoint0ycpfeeddirectionfeeddirectionFigure8.
Thelead-tiltsystem(lead=aandtilt=P)versustheinclination-screwsystem(inclination=eandscrew=(j).
Theabilityexiststoswitchfromoneangularsystemtoanotherusingtheseformulas:Table1.
TransistionformulasbetweenbothangularsystemsXinclination-screw=cosrp.
sin()X'ead-tilt=smaYinclination-screw=sinrp.
sin()Ylead-tilt=-cosa.
sinf3Zinclinalion-screw=cos()Zlead-tilt=cosa.
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