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附录A：英文资料AschematicdescriptionforproposedtoolpathgenerationandcontrolmethodisdepictedinFig.7.Intheproposedmethod.,compositecuttercontactdata,whichincludethesplinefunctionsfortheCClocation(C)andthesurfaceprinciplenormal(N),thepresetCCvelocity(cV),andthetoolinclinationandtiltangles(Φandλ),areloadedtotheCNCmachine.IntheCNCinterpolator,theCLpathiscalculatedinrealtimesoastomeetthedesiredCCvelocityalongtheCCpath.Consequently,thecutteroffsettingalgorithmisimplementedintheCNCinterpolator.AsisshowninFig.7,aglobalfeedbackloopisclosedbytheinterpolator,whichcanmonitorthepracticalCClocation(*C)inrealtimeandcompensateforthedeviationerrorfromthedesiredCCpath.Inaddition,on-lineadaptationofthefederate(i.etheCCvelocity)canbeintroducedtoaugmentthemachiningaccuracyandefficiency.Forinstance,wecanslowdownthemachining(byreducingcV)astheCCdeviationerrorincreasessignificantlyandspeedupthemachining(byreducingcV)asthedeviationerrorisalwaysnegligible.Noticethatavariablefederate(duetoon-lineincreasingofdecreasingcV)canbeadoptedonlywhenitdoesnotcauseunacceptabledegradationinotherfederate-dependentcuttingeffects,suchascuttingtime,toolwear,surfaceintegrity,etc.()(coscossincossin)ctccLCrNrrTNBrO（1）sincoscossinsinOTNB(2)11,sin()tan()xyzttooo（3）,,,,,,(,,)()tttttmmmmmxyzKinematicsxyz（4a）orsin()cos()sinsin()cossintmxmmymmmzmmmxbzlxlylz()cos()sintymmzmmylylzcos()sin()sincos()coscostmxmmymmmzmmmzbzlxlylz(4b)tm,tmand,,,,,,()(,,)mmmmmtttttxyzInvKinematicsxyz(5a)orcossinmxttttxlxzsinsinsincossincosmyztttttttttylbxyzcoscossinsincoscosmzztttttttttzlbxyz,mtmt(5b)(),(),(),(),()ttttttttttxxuyyuzzuuu（6）2212222222()2()llttttttkkttttttVhVhxxyyzzuuxyzxyz(7),,kkkttttuutuutuudxdydzxyzdududu222222,,kkkttttuutuutuudxdydzxyzdududu(8),,,,,,()(,,)rrrrrrrrrrmmmmmtttttRxyzInvKinematicsxyzThedesiredalgorithmsfortheproposedapproachtotoolpathgenerationandcontrolarepresentedinthefollowing.4.1CCpathinterpolation,cutteroffsetting,andinversekinematicsconversionThecorefunctionsfortheinterpolatoraretheCCpathinterpolation,thecutteroffsetting,andtheinversekinematicsconversion.LetthesplinefunctionsfortheCClocation(C)andsurfaceprinciplenormal(N)beexpressedby,,,cccCuxuyuzu,,xyzNuNuNuNu(9)whereuisthespatialparameteralongthespline.Theinterpolationalgorithmstatedintheabovesectionisutilizedhere.BecausetheinterpolationisconductedfortheCCoutputpath,ratherthantheCLpath,thesubscripttinEqs(7)andEqs(8)needstobereplacedbyc,whichcorrespondstotheCCpath.Besides,theCLvelocity(lV)inEq.(7)needstobereplacedbytheCCvelocity(cV).ThecutteroffsettingalgorithminEqs(1)andEqs(2)isalsosuitableforreal-timecutteroffsetting.NoticethatBTNandtheunittangentvectorTalongtheCCpathcancalculatedby11kkkkdCuCuCuduTdCuCuCudu(10)CAMComputationofpracticalCCpathinterpolatoraxialcontrolleraxialdriveaxialcontrolleraxialdrivemachineandprocesscompositeCCdata(C,N,Vc,Ф,λ)CNCC﹡RPFig.7.Proposedtoolgenerationandcontrolscheme.Throughthecutteroffsetting,thecutterlocationandorientationisavailable.Basedontheinversekinematicsconversion,whichisdepictedbyEq.(5c),wecangetthereferencecommandstothefiveaxialdrives,R.Inadditiontotheabovecorefunctions,twooptionalfunctionsthatincludereal-timecompensationfortheCCpathdeviationerrorandadaptationoftheCCvelocitycanbeintroducedtoaugmentthepracticalcontrolperformance.ThesetwofunctionsbasedonthefeedbackofthepracticalCCpoint,*C.4.2CalculationofpracticalCCpathIntypical5-axismachinetoolmotioncontrol,theavailablefeedbackdataaretheoutputpositionsalongthefiveaxes,whicharepmx,pmy,pmz,pmandpm.BasedonthedirectkinematicsconversionreferringtoEq.(4a)and(4b),wecangetthepracticalcutterlocation(**,LO)asComputationofpracticalCCpathinterpolatoraxialcontrolleraxialdriveaxialcontrolleraxialdrivemachineandprocesscompositeCCdata(C,N,Vc,Ф,λ)CNCC﹡RP

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