英语综述.docx
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英语综述.docx
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英语综述
Asdemandsfortheprecisionmachiningofthree-dimensionalsurfacesincreases,theevaluationofthemachinedsurfacetopologyandofthesurfaceroughnessbecomeamajorinterestinthemanufacturingprocess.Anincorrectdeterminationofcuttingconditionscancauseinferiorproducts,toolbreakagesandincreasesinmachiningtime,whichiswhyforthepastseveraldecadesanumberofstudieshavebeendonerelatedtothemodellingofmillingprocessesinordertoprovideoptimummachiningparameterswhicharesufficientforsurfacefinishcharacterisation.Forexample,therelationshipsbetweencuttingforcesandtooldeflectionhavebeenreportedandquiteafewoptimisationalgorithmsproposedbymanyresearchers.Thegeometricalscallopprofileshavealsobeenconsideredforthedeterminationofefficientandaccuratepathintervalsbetweensuccessivetoolpaths.Morerecently,Zhaoetal.analysedtheeffectofcuttertiltingangleonfinishedsurfaceroughnessandtextureinmulti-axismillingusingaZ-mapsimulation.Furthermore,theconceptsofoptimumandcriticaltiltinganglesforunidirectionalandbidirectionalfeedmachiningwereproposedintheirworks.
Inpart1ofthispaper,theprofilesoftherightridgeandtheleftridgewereanalysed,andtheequationsoftheirtrajectoriesandtheeffectivecutterradiusofeachridgeinthemaximumcutremaindersection,werederivedasfollows:
Inpart2ofthispaper,thepredictionsofthemaximumsurfaceroughnessandtheshapesofthecutremainderarepresentedfortheplanecuttingmodeofball-endmillingemployingtheridgemethod.Theshapesandheightsofthecutremainderareestimatedbyoverlappingadjacentridgeswhenconsideringthevariousmachiningparameters:
feedrate,pathinterval,andtwotypesofcuttingmodes.Themaximumsurfaceroughnessinplanecuttingmodesarederivedasafunctionofthemaximumeffectivecutterradius,Reff,max,andthepathintervalratio,τfpThepredictedresultsarecomparedwiththevaluesestimatedbytheconventionalroughnessmodel.Aseriesofexperimentsarealsoperformedtovalidatetheproposedmethodforvariouscuttingconditions.
2Predicitionofmachinedsurfacebytheridgemethod
Thefinaltopologyofamachinedsurfaceisgeneratedbyoverlapping
theshapesmachinedbyasinglecuttingpath.Therefore,thesurfaceroughnessandtextureofthemachinedsurfacecanbepredictedbycombiningthecharacteristiclinesinthemaximumcutremaindersectionpresentedinpart1ofthispaper.Inthissection,theproceduresarepresentedfortheevaluationofthemaximumsurfaceroughnessandthetextureofthemachinedsurfacebyball-endmillingintheplanecuttingmodeusingtheridgemethod.
Thereareusuallyphasedifferencesbetweenneighbouringcuttingpaths;therefore,themaximumcutremaindersectionsofadjacentpathsdonotcoincidewitheachother.Insomestudies[19,20],ithasbeenreportedthatthephasedifferenceimprovesthesurfacequalityandcanbeusedtocontrolthesurface
texture.However,itisverydifficulttocontrolthephasedifferenceinatypicalNCmachine.Furthermore,thephasedifferenceiscommonlyignoredintheconventionalroughnessmodel.Thusinthisstudythesurfaceroughnessandtheshapesofthemachinedsurfaceareevaluatedontheassumptionthattherearenophasedifferencesbetweenadjacentpaths.
Figure1showstwotypesofcuttingmodes,unidirectionalmodeandbidirectionalmode,forplanecuttingwithball-endmilling.Intheconventionalroughnessmodel,thetextureandsurfaceroughnessoftwomodesareestimatedtobeequalunderthesamemachiningconditions,buttheactualmachiningresultsareusuallydifferentfromeachother.Inthispaper,theunidirectionalmodeandbidirectionalmodeareanalysedinSects.2.1and2.2,respectively.
2.1Surfaceroughnessinunidirectionalmode
Inunidirectionalmode,therightridge,ψR,andtheleftridge,ψL,ofthecutremainderappearwithaperiodofpathinterval,fp,becausethecuttingdirectionsofsubsequentpathsdonotchange.Accordingly,theshapeofthecutremainderofthei-thcuttingpathisdeterminedbytherightridgeofthei-thpath,ψR,i,andtheleftridgeofthei+1-thpath,ψL,i+1.Thegeometricalconditionsfortheevaluationofsurfaceroughnessaremathematicallyclassifiedintothreetypeswithrespecttothepathintervalratio,τfp.Here,thepathintervalratiodenotestheratioofthepathintervaltothefeedpertooth,fp/ft.Figure2representsschematicdiagramsofallthecasesfortheunidirectionalmodeoftheplanecuttingmode.
Figure2ashowstheexpectedshapeofthecutremainderinthemaximumcutremaindersection,Π,whenthefeedpertoothislargerthanthepathinterval.Inthiscase,theprofilesofψR,iandψL,i+1donotmeeteachother,andthemaximumsurfaceroughnessofthearbitraryi-thpath,Hmax,ismathematicallyequaltotheheightoftheintersectionpointofthelinewhichisparalleltothetoolaxisandtheleftridgeofthei+1-thcuttingpath.
AsshowninFig.2a,therelationshipofthelength,δL,andthepathinterval,fp,isgivenby
ThesolutionofEq.3,φL,canbeobtainedbyanumericalmethod.Thenthemaximumeffectivecutterradius,Ru1eff,max,andthemaximumsurfaceroughness,Hu1max,arecalculatedby
wheresubscriptMdenotesthevaluescorrespondingtotheintersectionpointMandsubscriptsu1,u2andu3inthispaper
denote,respectively,Case(I),Case(II)andCase(III)inunidirectionalmode.
Equations4and5arederivedonthegeometricalassumptionthatHu1Mislowerthantheheightofthecutremainderattherotationalcentre,H0.ThegeometricalconstraintforCase(I)canbewrittenmathematicallyas
Accordingly,thecriticalpathintervalofCase(I)inunidirectionalmode,fu1pc,whichconfirmsCase(I)oftheunidirectionalmode,canbeobtainedby
wheresubscriptcinthispaperrepresentsthecriticalvaluesattheboundaryconditionsofeachcase.
SolvingEq.7revealsthatthecriticalpathintervalratioforCase(I)inunidirectionalmode,τu1fpc,isabout0.9262,sothecaseshowninFig.2aisapplicabletothemachiningconditioninwhichthepathinterval,fp,islessthan0.9262ft.
Case(II)oftheunidirectionalmodeisrepresentedinFig.2b.Inthiscase,theheightoftheintersectionpointoftwoadjacentridges,Hu2M,islowerthanH0.Thusthemaximumsurfaceroughness,Hu2max,isH0,sothemaximumeffectivecutterradius,Ru2eff,max,iscalculatedasfollows:
ThegeometricalconditionsatintersectionpointMcanbeexpressedas
HencethecriticalpathintervalofCase(II)canbeobtainedfromthegeometricalconstraint,Hu2M≤H0:
FromEqs.11and12itcanbeseenthatτfpc,Risabout0.6133andτfpc,LisascalculatedinthepreviousCase(I).SothecriticalpathintervalratioofCase(II)inunidirectionalmode,τu2fpc,isabout1.5395.Consequently,thecaseshowninFig.2bisobtainableunderthefollowingmachiningconditions:
0.9262ft≤fp≤1.5395ft.
ThefinalcasewhichcouldoccurinunidirectionalmodeisillustratedinFig.2c.Inthiscase,thepathintervalislargerthanthefeedpertoothcomparatively.Moreover,themaximumheightofthecutremainderistheheightoftheintersectionpointofthetwonearbyridges,ψR,iandψL,i+1,andiscalculatedbythefollowingsimultaneousequations:
Equations13and14canberewrittenasfollows,respectively
BysolvingEqs.15and16numerically,themaximumeffectivecutterradius,Ru3eff,max,andthemaximumsurfaceroughnessofCase(III),Hu3max,areobtainedby
3Predictedresults
Figure4aplotstheexpectedmaximumeffectivecutterradiusratio,τReff,max,againstthepathintervalratio,τfp,predictedbytheequationsdescribedinSect.2.Here,τReff,maxistheratioofthemaximumeffectivecutterradiustothefeedpertooth,Reff,max/ft.Figure4bshowstheratiosofτReff,maxpredictedbytheridgemethodtothevaluesevaluatedbytheconventionalroughnessmodel.Asshown,thedifferencebetweentworoughnessmodelsincreasesasthepathintervalratiodecreases.Itcanalsobeseenthatthegeometricalroughnessofthebidirectionalmodeisusuallylargerthanthatoftheunidirectionalmode.
Figure5ashowsthepredictedmaximumroughnessagainstthefeedpertoothfortheconditionsofatoolradiusof5mmandapathintervalof0.5mm.LikeFig.4b,Fig.5bpresentstheratioofthemaximumsurfaceroughnessexpectedbytheridgemethodtothevaluescalculatedbytheconventionalroughnessmodel.
4Experimentsanddiscussion
Tovalidatethemethodproposedinthisstudy,aseriesofexperimentsforvariouspathintervalratioswasconductedonaverticalthree-axismillingmachine.Theresultswerecomparedwiththesurfaceroughnesspredictedbytheridgemethod.
Forthetests,anuncoatedCBNball-endmillof10mmdiameterwithtworight-handedfluteswasemployed,andtheworkpiecematerialAI2024wasused.Machiningconditionswerechosentobe:
0.1mmdepthofcut,0.5mmpathinterval,0.1∼0.6mm/tooththerangeoffeedpertooth.Thespindlespeedwaskeptat2000rpm,andallthetestsweredonewithcoolant.ThecuttingconditionsusedintheexperimentalworkandtheexpectedsurfaceroughnessarelistedinTable1.
ThemeasuredmaximumsurfaceroughnessoftheactualmachinedsurfaceisshowninFig.6.Thereareafewdifferencesbetweenthemeasuredsurfaceroughnessandthepredictedvalues
Theerrorsmaybecausedbythephasedifferencebetweensubsequentcutterpathsanduncertainfactorsnotconsideredinthispaper,suchasbuilt-upedges,run-out,chipflow,etc.
Figure7showsthesurfacetexturesinthemaximum
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