FiabilitatesiDurabilitate-Fiability&Durabilityno2(6)/2010Editura“AcademicaBrâncuşi”,TârguJiu,ISSN1844–640X17ANALYTICALMODELOFCALCULUSFORINFLUENCETHETRANSLATIONGUIDEWEAROVERTHEMACHININGACCURACYONTHEMACHINETOOLAssoc.prof.dr.eng.IvonaPETRE,UniversityValahiafromTargoviste,Lecturerdr.eng.CarmenPOPA,UniversityValahiafromTargoviste,Lecturerdr.eng.DumitruDUMITRU,UniversityValahiafromTargoviste,Eng.CiprianMANESCU,UniversityValahiafromTargoviste,Abstract:Thewearofmachinetoolsguidesinfluencesfavorablytovibrations.Asaresultofguideswear,theinitialtrajectoryofcuttingtoolsmotionwillbemodified,thegeneratingdimensionalaccuracydiscrepanciesanddeviationsofgeometricalshapeoftheworkpieces.Asithasalreadybeenknown,thewearofmobileandrigidguidesisdeterminedbymanyparameters(pressure,velocity,frictionlength,lubrication,material).Thechoiceofoneoranotheranalyticmodeland/ortheexperimentalmodelofthewearisdependingbytheworkingconditions,assumingthatthecouplingmaterialisknown.Thepresentwork’sgoalistoestablishananalyticmodelofcalculusshowingtheinfluenceofthetranslationguideswearoverthemachiningaccuracyonmachine-tools.Keywords:accuracy,machine-tools,surface.1.IntroductionAsithasalreadybeenknowntheaccuracyofmachiningeachpiecedependsonamultitudeoffactorsconnectedtothetechnologicalsystem(themachinetool,theclampingdevice,thecuttingtooletc)[1,2,3].Inthepresentwork,theauthor’sgoalistoestablishthesizeandinfluenceonlyofthewearofthebedtheslideguideoverthemachiningaccuracyonmachine-toolswithuseonlather.Thesizeoftheguideand(longitudinal)slidewearareimportanttobeknownbecausethechangeoftheslidetrajectoryduetothewearthatoccursintimeconditionsthedimensionaldeviationsandthequalityofthemachinedpartssurface.Inordertoestablishthewearsizeofthesystembed-slide,threedistinctsituationsarebeinganalyzed:1–thebedguideonlyisbeingworn2–theslideguideonlyisbeingworn3–bothguides(bed-slide)arebeingworn2.Analyticmodelsestablishingtheerrorproducedbythebed-slideswearInordertoestablishthequantitativeinfluenceofthewearprocessoverthemachiningaccuracyonalathe,thefollowingassumptionsaremade[2]:-thecurveofthewornprofileoftherigidguideU(x)isconsideredknownatacertainmomentassessedbythenumberofthestresscycles;-thewearonthecurrentstresscyclesisneglectedcomparedtothewearproducedbyallthepreviouscycles;-themobileguidewearU1(l)issoproducedthattheprofileofthisguidefollowscontinuouslytherigidguideprofile;basedonthisassumptionitisadmittedthatthecontactisalwaysofthetypeaccordingtotheappropriatedistributionofthenormalandtangentialstress;-themobileguideissetontherigidoneduringthedisplacementsothatnormallinetothecontactsurfaceofthetwoprofilesisunique;-thewearisacontinuousprocessandischaracterizedbythethicknessofthewornlayer,consideredasacontinuousfunctionontotheguidelengthandintime.FiabilitatesiDurabilitate-Fiability&Durabilityno2(6)/2010Editura“AcademicaBrâncuşi”,TârguJiu,ISSN1844–640X18Basedontheseassumptionsthewearofthebedandslideguideisestablishedforthe3situationshowninthefirstpartofthework.Case1:thebedguideisbeingonly(fig.1)xoxABCOUthebedguidetheslideguideUxoFig.1.Settlementschemeofthemobileslideonabed-guideTakingapointA(xo,Uxo)situatedatthemiddleofthemobileslide.ThewearofthebedguideintheconsideredpointisUxoandthefunctionofthebedguidewearUx.ThedeviationofthepointAisconsideredAC1=∆.Inordertoestablish,thecoordinatesofthepointCthenormalatthebedguideprofileinthepointAisconsideredastraightlinewiththeslopemthatcanbedeterminedbasedonthewearfunctionUx.nmxy+=(1)'xMU/1m−=(2)Where:nxU1U'xx+−=andxU1Un'xx+=Beingtheconditionstolimit,theco-ordinatesofthepointCwillbe0yc=andxUUx'xxc+=.Thedeviationinthiscaseconsidered:()()()adm2'xx2Ac2Ac1U1Uyyxx∆≤+=−+−=∆(3)Case2:theslideguideonlyisbeingwornaccordingtoalinearvariationlaw(fig.2).ConsideringthepointB(0,b)situatedatthehalfoftheslidewiththelengthl.Afteracertainperiodoffunctioning,asaresultoftheslidewear,thepointBwillbedisplacedinthepointB’.Inthissituationthedeviationofthepointwillbe:'BB2=∆Inordertomakethecalculationofthisdeviation2casescanbedistinguished:a)thepointAisnotworn0UA=;b)thepointAiswornbyasizethatcanbeestablished(measured)0UA≠aalB(0,b)B'SlideBedC'MO'OCA(a,0)Fig.2.AssessmentschemeofthemobileslidegeometrychangesFiabilitatesiDurabilitate-Fiability&Durabilityno2(6)/2010Editura“AcademicaBrâncuşi”,TârguJiu,ISSN1844–640X19•StaringfromtheequationofthestraightlinethatgoesthroughthepointsAO’andfollowingthesomeargumentasincase1,thedeviationofthepointB’willbe:-for0UA=⇒2/cosba2222α⋅+=∆-for0UA≠⇒2/cos)Ub(a2'2A22α⋅++=∆Thesizeoftheangleαdependsonthesizeoftheaccuracydeviationimposedtotheslide:lUAMMCtgc==α(4)TheangleαcanbeknownifthewearofthepointC,Usandadmααaremeasured(known).Theallowablesizeoftheangleadmαisasizethatcanbeestablishedfromtheaccuracyconditionsimposedbythemachinetoolonwhichtheslideisinstalledwhere:lAAAlAtgippira+==α(5)where:Ai–theinitialdeviationthatcanbeacceptedasbeingthemaximumallowabledeviationprescribedwithintheaccuracyparametersofthemachine-tool;App–theaccuracydeviationallowableofthepartsmachinedonthemachinetool;Ara–theallowablerelativedeviationofaccuracy