数控技术 河南科技大学教案 英文版

河南科技大学教案首页课程名称

数控技术（双语）

任课教师

韩建海Chapter2

NCPartProgramming

计划学时

8教学目的和要求：

Bylearningthecontentsofthischapter,studentswillgraspthebasicsofNCprogramming;masterthemanualprogrammingmethodsandtechniquesofNCmillingmachine,NClathe,NCmachiningcenters;understandthenumericalcontrolprogramminglanguage,processandmethodsofgraphicalprogramming.重点：1.BasicknowledgeofCNCprogramming:programmingcontentandsteps,programmingmethods,NCMachiningProcess2.Manualprogramming:Gcode,Mcodeandothercode,holemachiningprogramming,turningprogramming,contourmillingprogramming.

难点：

1.Thecharacteristicsandskillsof

NCTurningandNCMillingprogramming.思考题：1.Glossary:NCprogramming,workcoordinates,toolcoordinates,partcoordinatesystem,theabsolutecoordinatesystem,therelativecoordinatesystem2.WhataretherequirementsofISOstandardontheCNCmachinetoolcoordinatesystem?3.Whatarethebasepointsandnodepoints?4.WhatarethecharacteristicsofNCTurningprogramming?

内容提要ThischapterwillelaboratetheCNCmachiningprocessanalysisandthetypicalprocessingmethods;themethodsofestablishment,structureandcommonlyusedalgorithmsofNCprogram;andmakeabriefoftheautomaticprogramming.Chapter2

NCPartProgramming2.1

INTRODUCTION

Theprogramofinstructionsisthedetailedstep--by--stepcommandsthatdirecttheactionsoftheprocessing

equipment．In

machinetoolapplications，theprogramofinstructionsiscalledapartprogram，andthepersonwhopreparestheprogramiscalledapartprogramNumericalcontrol(NC)isaformofautomaticallyoperatingamachinetoolbasedoncodedalphanumericdata.Acompletesetofcodedinstructionsforexecutinganoperationiscalledaprogram.Theprogramistranslatedintocorrespondingelectricalsignalsforinputtoservomotorsthatrunthemachine．

Wecallthewholeprocessfrompartgraphicstofinishingcontrolmediumtheprogrammingofnumericalcontrolmanufacturing,orcallitNCProgramming.Whenusingnumerical’controlmachinetooltomanufactureparts，theprogrammingisveryimportant．Theprogramisnotonlycorrectandfastbutalsoeffectiveandeconomic．2.1.1TheContentsandStepsofNumericalControlProgramming

BeforeNCprogramming，theprogrammershouldunderstandthenumericalcontrolmachinespecifications,characteristics,thefunctionsandprogramminginstructionformatofthe

CNCsystem，etc．Whenprogramming，heshouldanalyzethepart’stechnicalrequirements，geometricalshapedimensionsandtechnologicalrequirements.Thenhecandeterminethemanufacturingmethodandcalculatenumericalvalue,getcutterposition,Accordingtopartdimension，cutterpositionvalue，cuttingparameters(spindlespeed，feed-rate，cuttingdepth)andauxiliaryfunctions(ATC，CW，CCW，coolantonandoff)，theprogrammercanprogram．TheprogramcanbeinputtedintoCNCsystemandtheCNCsystemcontrolsCNCmachinetoolstomanufactureautomatically．

Generallyspeaking，themainstepsofNCprogrammingareanalyzingpartgraphics，determiningthemanufacturingtechnologicalprocess,calculating,numericalvalue，programming，verifyingtheprogramandinputtingtheprogramintoCNCsystem．Figure2．1illustratestheprogrammingsteps．

(1)Analyzingpartgraphicsanddeterminingthemanufacturingtechnologicalprocess

Thisstepincludesanalyzingthepartgraphics，understandingthemachiningcontentsandrequirements，thendeterminingtechnologicalprocesses，machiningplans，machiningsequence，machiningroutes，fixingmethods，cuttingparametersandselectingcuttingtools，etc．Besidesthese，thenumericalcontrolmachinecodesshouldbeunderstoodclearlyandthenumericalcontrolmachinefunctionsshouldbeexploitedfully．

(2)Correctlyselectingprogramoriginandcoordinatesystem

Innumericalcontrolmachinetoolsmanufacturing，correctlyselectingprogramoriginandcoordinatesystemisveryimportant．OnNCprogramming，theprogramcoordinatesystemisthestandardC00rdlnatesystemascertained0ntheworkpiece.

(3)Calculatingnumericalvalues

Afterfinishingthetechnologicalprocess，thenextstepistogetthetoolpathaccordingtopartgeometricdimensionandthemethodofcutterradiuscompensation，SOwewillobtainthecutterposition．

(4)Writingpartprograms

Afterdeterminingmachiningroute，technologicalprocessandthecoordinatevalueoftoolpath，step-by-step，theprogrammercanwritetheprograminaccordancewiththespecifiedfunctioncodesandprogramformatofCNCsystem．

(5)Fabricatingcontrolmedium

TheProgramiscoded0nasuitablemediumforsubmissiontothemachinecontrolunit．formanyyears，thecommonmediumwas1-inchwidePunchedtape，usingastandardformatthatcouldbeinterpretedbythemachinecontrolunit．Today，punchedtapehaslargelybeenreplacedbynewerstoragetechnologiesinmodernshops．Thesetechnologiesincludemagnetictape，diskette，andelectronictransferofpartprogramsfromacomputer．

(6)Verifyingpartprograms

Beforetheprogramisusedinrealproduction，wemustchecktheprogram．Wedetecttoolpatherrorsthatcouldruinthepart，damagethefixtures，breakthecuttingtoolorcrashthemachine，etc．Insomecases，wetesttheprogramthroughmanufacturingapartonamachine．Onthebasisofdetectingresult，theprogramisneededtobemodifiedandtobeadjusteduntiltheprogramsatisfiesthemachiningrequirementscompletely．

Thestepsabove-mentionedareprogrammedmanually．Thisprogrammingmethodiscalledmanualpartprogramming．Andwealsoknowthataprogrammernotonlymusthavetheknowledgeofthestructureofmachinetools，thefunctionsandstandardsofCNCsystem，butalsohavetheknowledgeoftechnologicalprocess，suchasfixtures，cuttingtoolsandcut-tingparameters，etc．2.1.2TheMethodsofNCProgramming

Partprogrammingcanbeaccomplishedusingavarietyofproceduresrangingfrommanualmethodtohighlyautomatedmethod．

(1)Manualpartprogramming

Theprogrammingiscalledmanualpartprogrammingwhichwholepartprogrammingiscompletedmanually(includingcalculatingnumericalvalueonacomputer)．

Inmanymechanicalmanufacturingtrades，therearealargenumberofuncomplicatedpartsthatareconstitutedonlybythesimplegeometricelementsofstraightlinesandcircles．Thenumericalvaluesofthepartsarecalculatedsimply．Theblocksofaprogramaren’tlot．Andcheckingtheprogramiseasy．Thesepartprogramscanbecompletedmanually．Somanualprogrammingisstillaverycommonprogrammingmethodathomeandabroad．

Butmanualprogramminghasdifficultyorimpossibilitytoprogramcomplicatedpartsthathavenon-circularcurvesandsurfaces．Sowemustusetheautomaticpartprogrammingtoprogram．

(2)AutomaticprogrammingAutomaticprogrammingisalsocalledcomputer-aidedProgramming.Mostorallofthe

programmingiscompletedbyacomputer，suchascalculatingnumericalvalues，writingprograms，fabricatingthecontrolmedium，etc．Automaticprogramminglightensprogrammerintensityoflabor，shortenstheprogrammingtimeandimprovestheprogrammingquality．Atthesametime，itsolvesthecomplicatedpartprogrammingwhichisimpossibletoprogramby

manualprogramming．Themorepartsarecomplicatedshapeandtechnologicalprocess，the

moresuperiorityofautomaticprogrammingclearis．

Therearemanymethodsofautomaticpartprogramming．Accordingtothedifferencesofinputprogrammingmessageandhandlingstylesbyacomputer，theyaredividedintoautomaticallyprogrammedtool(APT)basedonautomaticprogramminglanguageandpartprogrammingusingCAD/CAM(computer-aideddesign/computeraidedmanufacturing)based

oninteractivegraphicssystem．ACAD/CAMsystemisacomputerinteractivegraphicssys-temequippedwithsoftwaretoaccomplishcertaintasksindesignandmanufacturing.

2.1.3TheBasisofNCPartProgramming2.1.3.1TheGeometricBasisofNCPartProgramming

(1)NCCoordinatesystems

ThelocationofaCNCMachinetoolsatanytimeiscontrolledbyasystemofXYZcoordinatescalledCartesiancoordinates．Thissystemiscomposedofthreedirectionallines，calledaxes，mutuallyintersectingatanangleof90．Thepointofintersectionisknownastheorigin．Thoseaxissystemstandardsinclude：

(i)Primarymachineaxesofmovement：shouldfollowtheright-handrule.SeeFigure2.2.

(ii)SpindlemovementisprimarilyalongtheZax-is．Movementintotheworkpieceisalongthe-Zaxisandmovementawayfromtheworkpieceisalongthe+Zaxis．

(iii)Inamajorityofmillingmachines，motionalongtheXaxisisthelongesttravelperpendiculartoZ．TheXaxisisparalleltotheworkholdingandisinthehorizontalplane．The+XaxismovestotherightalongaplaneO{theworkastheoperatorlooksatthatplane．

(iv)Withregardtomillingmachines，motionalongtheYaxisistheshortesttravelperpendiculartoZ．TheYaxisisinthesameplaneastheXaxis．Lookingattheplane，theoperatorwillnotethattheYaxisisperpendiculartotheXaxis．

MostCNCmillingmachinescanperformsimultaneousmotionsalongtheX，Y，andZaxesandarecalledthree-axismachines．SeeFigures2．3andFigure2．4．

MorecomplexCNCmachineshavethecapabilityofexecutingadditionalrotarymotions

asfollows：●RotationaboutanaxisparalleltotheXaxisorA-axisrotation●RotationaboutanaxisparalleltotheYaxisorB-axisrotation●RotationaboutanaxisparalleltotheZaxisorC-axisrotationRotarymotiondirectionsalsofollowtheright-handrule．SeeFigure2．5andFigure2．6．

(2)Programzeropoint

Theprogrammingzeropointisrelatedtotheoriginpositiononthegraphics．Itisalogicalreferencepointfromwhichtowork．Sotheprogrammermustdecidewheretheoriginof

thecoordinateaxissystemshouldbelocated．Thisdecisionisusuallybasedonprogramming

Convenienceandfindingeasiness．Forexample，theoriginmightbelocatedatoneofthecornersofthepart．Iftheworkpartissymmetrical，thezeropointmightbemostconveniently

definedatthecenterofsymmetry．Whereverthelocationis，thiszeroiscommunicatedtothe

machinetooloperator．Atthebeginningofthejob，theoperatormustmovethecuttingtool

undermanualcontroltosometargetpointontheworktable，wherethetoolcanbeeasilyand

accuratelypositioned．Thepartprogrammerhaspreviouslyreferencedthetargetpointtothe

originofthecoordinateaxissystem．Theoperatorinputsthecoordinatevalueofzeropointtothemachinecontrolunit(MCU)．

(3)Typesoftoolpositioningmodes

Withinagivenmachineaxescoordinatesystem．amachinetoolcanbeprogrammedtolo-caretoolpositionsinthefollowingmodes：absolutemode，incrementalmode，ormixed(absoluteandincrementalmodes)．

(i)Absolutemode

Whenoperatinginthismode。themachinetooldetermineseachnewtoolpositionfromahomeorspecifiedorigin(0，0)．RefertoFigure2．7(a)．

(ii)Incrementalmode

Machinetoolsoperatinginthismodelocateeachnewtoolpositionbymeasuringfromthelasttoolpositionestablished．SeeFigure2．7(b)foranillustrationofincrementalposition．IncrementalcoordinatesareusuallystoodforU，V，W.TheaxisofU，V，Wparallelsthe

axisofX，Y，Zrespectivelyandinthesamedirection．IfthetoolpathisfromAtoB，theCoordinates

ofAandBrespectivelyisUA-0，VA-0，UB-20，VB-30．ThecoordinatesystemofU-Visincrementalcoordinatesystem．

Incrementalpositionhassomedrawbacks．Themostnotableisthatifoneincrementalmovementisinerror，allothersubsequentmovementswillalsobeincorrect．Modernmachinetoolshavetheabilityofoperatingineitherpositionmode．Accordingtotheactualsituation，theprogrammercanuseabsolutemodeorincrementalmode．2.1.3.2

TheTechnologicalBasisofNCProgramming

ThetechnologicalhandlingisaveryimportantjobinCNCpartprogramming．Itaffectswhetherthepartprogramsarevalidandrationalornot．SincetheCNCmachiningprocessisautomaticunderthepartprograms，thevalidityandrationalityofthepartprogramsarerequiredveryhigh．Otherwisethequalifiedproductsaren’tmanufactured．Beforepartprogramming，theprogrammermustchoosethemachiningprocess，technologicalroutes，cuttingtoolsandcuttingparametersvalidlyandrationally．

ThetechnologicalhandlingofCNCmachiningisthesamewiththatofcommonmachininginthemain，butithasitscharacteristics．Generallyspeaking，CNCmachininghascomplexworkingprocedures．Atanymomenttheoperatorofcommonmachinescanhandlemanysituationsagilely．ButCNCmachinesareoperatedunderthearrangedpartprograms．ThecontentoftechnologicalhandlinginCNCmachiningincludes：analyzingtherationalityofCNCmachiningandthetechnologiesofparts，determiningthetechnologicalroutes，themethodsofpartfixing，selectingcuttingtoolsanddeterminingthecuttingparameters，etc．AccordingtothecharacteristicsofCNCmachining，discussingsomeproblemsshouldbepaidattentioninCNCmachiningasfollow．

(1)Determiningthepartmachiningroutesrationally

Thepartmachiningroutesarecuttingtoolmovementpathanddirectionrelativetothepartthatismachined．Theprinciplesofdeterminingthepartmachiningroutesinprogramminginclude：

(i)Guaranteeingtherequirementsofmachiningprecisionandsurfaceroughness；(ii)Shorteningmachiningroutesandreducingthetimeofidletoolrunningasmuchaspossible；(iii)Simplifyingthenumericalvaluesandreducingtheprogrammingblocks．

WhenCNCmachinetoolswork，themillingmaybeclimbmillingorconventionalmillingaccordingtothedifferenttoolmovementpathanddirection．Ifthemillingwaysaredifferent，thepartsurfaceroughnessisdifferenttoo．Sothemillingwaysshouldbeselectedrationally．Generallyspeaking，conventionalmillingisusedinroughmachiningandclimbmillingisusedinprecisionmachining．

Becausethemachiningprocessisatthebalanceofelasticitydeformationstatus，thetoolpausecancausethecuttingpowerchangessuddenly．AndthetoolmarkwillbeleftonthesurfaceofDart．Sothetoolpausemustbeavoided．Ifthereisalotofallowanceonthepart，thetoolcancutrepeatedly．Asmallquantityoffinishmachiningallowanceshouldbeleft，a-bout0．2～0．5mm．

(2)Selectingtoolsettingpointandtoolchangingpointrationally

Whenaprogramiswritten，toolsettingpointandtoolchangingpointshouldbeselectedvalidlyandrationally．Thetoolsettingpointisthebeginningpointofmovementrelativetotheworkpiecewhenamachinetoolmanufacturesapart．Theprogramisexecutedfromthepoint．Toolsettingpointcanbeselectedonoroutsidetheworkpiece．Butithasthedimensionrelationwiththeworkpiecepositiondatum．Theprinciplesofselectingthetoolsettingpointare：

(i)Thesettingpointmakesoperatingeasilyandprogrammingsimply；

(ii)Thepointiseasytofind；

(iii)Thecausedmachiningerrorissmall

Thetoolpositiononamachineisexpressedbythepositionoftoolpositionpoint．ThetoolpositionPointsofvarioustoolsaredifferent.ThePointsoflathetoolandboretoolarenoseofthetool；thepointofendmillisthecenterofthetool；andthepointofaballendmillisitsballnose．SeeFigure2．8．Whenamachinetoolwithatoolmagazineneedstochangetoolsatmachiningprocess，thetoolchangingpointshouldbeset⑥．Thetoolchangingpointisthepositionofchangingtools

bycutterframe．Thepointmaybeafixedpoint(suchasthemanipulatorofmachiningcenter)orasetpoint(suchaslathecenter)at

will.

Thecutterchangingpointshouldbesetonthework-pieceoroutsidethefixture．Theprincipleofsettingchangingtoolpointisthatthecutterframecan’ttouchworkpieceandotherpartswhenitchangestools．

(3)Rationallyselectingthemethodsoffixing，cuttingtoolsandcuttingparametersThefixingmethodsofCNCmachinesarethesameasthatofcommonmachines．Universalfixturesshouldbeselectedasfaraspossible．Andthefixingtimeshouldbereduced．Machiningsurfaceshouldbemanufacturedatonetime．Selectinganddesigningofthefixturesfollowtheprinciplesasfollow．(i)Selectingstandardandcommonfixturesasfaraspossible，avoidingselectingspecialfixtures；(ii)Fixingandremovingpartsquickly，convenientlyandrationally；(iii)Thepartsurfacetobemachinedshouldbeexposedtooutside．Don’tletthefixtureaffecttherapidmotionandmachiningofatool．Whenaprogrammerprograms，rationallyselectingcuttingtoolsisaveryimportantjob．Itaffectsnotonlytheefficiencyofmachinetools，butalsothequalityofparts．Whencutting

toolsareselected，thematerialofworkpieces，thetypesofsurfacetobemachined，theabilityofthemachinetoolandthecontentsofworkingprocedureshouldbeconsidered．Theselectingprincipleissimilartothetraditionalselecting．ButthecuttingtoolsrequirementsofCNC

machiningaremuchhigher．Thecuttingtoolsmustbeofhighprecision，betterrigidity，andlongdurability．Andtheirdimensionisstabile．Thecuttingtoolsshouldbefixedandadjustedeasily．

Thecuttingparametersincludespindlespeed，feedrate，cuttingdepthandcuttingwidenessetc．Thedifferentcuttingparametersareselectedaccordingto

thedifferentmachinemethodsandmaterialsofworkpiece．

Atroughmachining，thefirstthingshouldbeconsideredisefficiency．Butthecostof

machiningshouldbeconsideredtoo．Athalf-finishmachiningandfinishmachining，thequalitymustbeensured．Theefficiencyandmachiningcostaregivenconsideration．Thesearethe

principlesofselectingcuttingparameters．

2.2

THECODESUSEDINCNC

Therearemanycodesincludedinaprogram．PreparatoryfunctionsareGcodesandauxiliaryfunctionsareMcodes．TheyarethebaseofCNCprograms．ISOhasworkedoutthe

standardsofGcodesandMcodes．BecausenewCNCsystemsandmachineshavebeenemerging，alotoffunctionsinmanysystemssurpassISOstandards．Theircodesareabundantandtheirformatsareflexible．Theyaren’trestrainedbyISOstandards．Inaddition，evenifthesamefunction，itscodeandformathavealotofdifferencesamongsystemsmadeindifferentcompanies．Andcodesandformatsalsohavedifferencesbetweennewandoldsystemsmadeinthesamecompany．ButthepreparatoryfunctionscodesandauxiliaryfunctionscodesinmostofCNCsystemsareuptoorsimilartotheISOstandards．BeforeintroducingtheGcodesandMcodes，wemustunderstandprogramminglanguageformatsfirst．2.2.1ProgrammingLanguageFormat

AprogramformatisasystemofarranginginformationsothatitissuitableforinputtoinXand40plusinYfromthebeginningpointAofthemotion．Theblockis：

N20G9lG01X-30.Y40.F100.；

(ii)AssigningtheworkcoordinatesystemG92

G92belongstofixtureoffsets．Fixtureoffsets，alsocalledworkcoordinatesystemmultiplesettings．allowtheusertoworkwithseveralcoordinatesystemswithinthesameprogram．Whenitisconvenient，ifnotmandatory，theprogrammerisabletosetupmorethanonecoordinatesystemintheprogram．Herearesomeexamples：

First，therearetimeswhenitisnecessarytomachinemorethanoneworkplaceinasetup．Thedegreeofsimilarityofworkplacestobemachinedcanrangefromidenticaltocompletelydifferent．Theremayalsobedifferentoperationsonthesameworkplacetobeperformedwhileseveralworkplacearebeingheldatdifferentattitudesinasetup．Havingtheabilitytoassignmorethanonecoordinatesystemmakesiteasytogofromoneworkplacetothenextandstillbeabletorefertoprintdimensions．

Second，whenaworkplacetobemachinedmustbeheldinarotarydeviceofsomekinds，especiallyonhorizontalmachiningcenters．Itmaybenecessarytoworkontwoormoresidesoftheworkplaceinthesamesetup．Fixtureoffsetsallowtheprogrammertoassignoneprogramzeropointforeachsideoftheworkplacetobemachined.

Figure2.12illustrateshowtoassignworkcoordinatesystem．(a)istheexampleof

turningcenter．Theblockofformatis：

N20G92X400

.Z100.

(b)istheexampleofmachiningcenter．Theblockofformatis：

N20G92X180.Y20.；

(iii)SelectingworkcoordinatesystemcommandsG54--G59

G54-G59areseparatelycalledworkcoordinatesysteml，workcoordinatesystem2…workcoordinatesystem6.ThesixworkcoordinatesystemsareassignedthroughsettingtheoffsetsfrommachinecoordinatesystemoriginontheCRTpanel．

Aprogrammercanchooseanyoneofworkcoordinatesystems．G54-G59commandsareusedtoassigntheprogramzeropoint．Itisalsoafixtureoffsetcommandthattellsthecontrolwhichcoordinatesystemtobeused．Remember，therearetwowaystoassignprogramzero：G54—59andG92.OurgivenformatusesG54--G59.IfyouareusingtheG92commandtoassignprogramzeroyoucansubstituteG92(X，Y，Z)fortheG54givenintheprogramstart—upformat．ThevaluesincludedinX，Y，andZmustreflectthedistancesfromprogramzerotothereferencepoint．IfG92

isused，

G54--G59commandswillappearintheprogram．Whenyouusefixtureoffsetsandespeciallywhenyouusemorethanone，werecommendincludingthecurrentfixtureoffsetcommandaspartOfeachtool'sstart—upformat．Figure2.13illustrateshowtoselectingworkcoordinatesystem2(G55)．Theblockis：N1OG90G55G00

X60.Y40.；(2)SelectingplanecommandsG17，G18andG19

Thethreemutualperpendicularaxes(X，Y，Z)inCartesiancoordinatesystemconstructthreeplanes．TheyareXYplane，XZplaneandYZplane．Machiningcenterselectsthesecommandstocontrolmachiningontheseplanes．BecauseturningcenterusuallymachinesonXZplane，theselectingplanecommandisnotneed．G17illustratesmachiningonXYplane．G18illustratesmachiningonXZplane．G19illustratesmachiningonYZplane．SeeFigure2.14.

(3)TheGcodesrelatedtotoolmovement

(I)RapidmotionG00

ThistypeofcommandisusedtopositiontheCNCmachinetoalocationwheresomeactionistooccur．Undernormaloperation，theG00commandwillcausethemachinetomoveatitsfastestpossiblerate．Therapidrateswillvaryfrommachinetomachine．SeveralcurrentCNCmachinesboastrapidrates—wellover24MPM．Themachinewillbemovingveryquicklywhileundertheinfluenceofarapidmotioncommand．

Figure2.15showsasketchofhowrapidmotionwillOccur．Inthisexample，weintend

thetooltomoverapidlyfromthestartingpositiontotheendingposition．Intheabsolute

mode，thiswouldbecommandedbythefollowingcommand：

N005G00X80.Y50.；Notethattheabovecommandwillbecorrectonlyintheabsolutemode，commandedbyG90onmostcontrols．Intheincrementalmode(G91)，theaxisdepartures(X，Y，Z，etc．)

would

betakenformthetoolscurrentposition.Dependingonwhattheprogrammerintendstodointhecommand，anynumberofaxisdeparturescanbeincludedintheG00command．Theprogrammercanmakethemachinemoveinoneaxisonlyoramotioncanbemadeintwo0rmoreaxessimultaneously．Iftheprogrammerwishesthemachinetomoveinonlyoneax—is，onlyoneletteraddress(X，y，Z，etc．)andthevalueofthedepartureneedtobeincludedintheG00command．AxesofletteraddressesnotincludedintheG00commandwillnotmoveduringtheexecutionofaG00command．

(ii)G0llinearinterpolation(Straight-Linemotion)

Thesecondtypeofmotionwewilldiscusscausesthemachinetomovealongaperfectlystraightpathinoneormoreaxes．Thecontrolwillcalculatethepathbetweenthestart

pointandtheendpointofthemotionautomatically，nomatterwhatangleisinvolved．

TotrulyunderstandhowcombinedaxismotionOccurs，youmustunderstandthewordinterpolation．Forexample，whenthecontrolmakesastraightmotionintwoaxes，calledlinearinterpolation．a11thatisrequiredisthestartpointandtheendpointofthemotion．Thecontrolfillsautomaticallyandinstantaneouslyinthemissingpointsbetweenthestartpointandtheendpoint⑩．Whatreallyhappensisthatthecontrolmakesaseriesofverysmallone—axismovementsfromthestartpointtotheendpoint.Thisseriesof

motionsresembles

astairway．Eachstepalongthewayisverysmall，andtheendresultwillappeartobeaperfectlystraightline．Figure2.16shows

apictureofwhatactuallyhappensduringlinearinterpolation．

AsyoucanseefromFigure2.16whentwoormore

axesareprogrammed，thecontrolformsaseriesofsmallone—axismovements．Thesizeofeachstepdeterminestheresolutionoftheaxis．Thesmallerthestep，thebettertheresolutionis．ThedrawinginFigure2.16intentionallyexaggeratesthesituation．

Alsoofnoteregardingthelinearinterpolationcommandisthemotionrateatwhichtheaxeswillmove．Thismotionrateisprogrammeddifferently，dependingonthestyleandapplicationofthemachine．Metalcuttingmachines，likemachiningcentersandturningcenters，useanFwordtospecifythedesiredfeedrateforthecommand．EvenwithanFword，itmaybepossibletospecifythefeedrateinoneoftwoways．Oneisfeedperminuteandtheotherisfeedperrevolution．Intheinchmode，thisequatestoinchesperminuteandinchesperrevolution．Inthemetricmode，thisequatestomillimetersperminuteandmillimetersperrevolution.

(iii)CircularinterpolationG02andG03

Circularinterpolationisperformedmuchthesameway．NotethesimilarityinFigure2.17.Bycontouring，wemeanmakingmotionsaroundtheperipheryofashape．Contouringcanincludestraightlineandcircularmotion.CircularinterpolationinvolvestwoGwords．ThereasonwhytherearetwoGwordsistoallowtheprogrammertospecifythedirectionofthecircularmotiontobemachined．Clock

wisemotion(CW)orcounterclockwisemotion(CCW)．Todeterminewhetheraparticularmotionisclockwiseorcounterclockwise，theprogrammermustlookatthemotionfromtheplussideoftheuninvolvedaxis．IfmakingacircularmovementinX-y，lookatthemotionfromtheZplusside．IfmakingacircularmovementinX-Z，lookatthemotionfromtheY

plusside，andsoon．

Figure2.18illustratesG02andG03.G02representsclockwisemotionandG03representscounterclockwise．

LiketheG0llinearinterpolation，therateofmotioncanbecontrolledduringacircularmovement．AllinformationpresentedaboutfeedratecontrolforG01stillappliestoG02andG03.AlsolikeG01，theG02andG03commandsrequirethattheendpointofthecircularmotionbeincludedinthecircularcommand．Thecontrolassumesthatthecurrentpositionofthetoolisthe