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TemperatureFieldAnalysisandExperimentalTestofCNCLathePrecisionSpindleSystemwithoutLoadLixiuZhang1,a,QinghuaShi2,bandYuhouWu3,cShenyangJianzhuUniversity,Shenyang110168,Chinaa851617088@qq.
com,b474891749@qq.
comKeywords:mechanicalspindle;thermalanalysis;temperaturefield;thermalbalancetime.
Abstract:ThearticleisbasedonprecisionCNClathespindlesystemofthe170CP06astheresearchobject.
Thesteadyandtransienttemperaturefieldmodelofthemechanicalspindleisestablishedbyusingthefiniteelementanalysismethod.
Astheheatratefortheloadandtheconvectiveheattransfercoefficientfortheboundaryconditionsforthermalanalysis,thetemperaturefieldofspindlesystemisinvestigatedtogetthesteadystatetemperaturefielddistributionandthermalbalancetimeofthespindlesystem.
Inordertoverifythecorrectnessofthemodel,thethermalexperimentswithoutloadareexecutedtothekeypartsofthetemperatureofthespindlesystematdifferentspeeds.
Comparedwiththesimulationresults,ithasaverygoodagreementwiththereliabilityofthemodel.
Anditprovidesatheoreticalbasisforcontrollingthetemperatureriseofthespindlesystem.
IntroductionWiththerapiddevelopmentofmodernmachinerymanufacturingtechnology,therequirementsofmachine'saccuracyarealsobecominghigherandhigher.
Inthehigh-speedandprecisionmachinetools,theproblemofmachiningerrorcausedbythermaldeformationalsohasbecomeincreasinglyserious.
Alargenumberofexperimentalstudiesshowthethermalerroristhelargesterrorsourceofmachinetoolsaccountingfor40%to70%inthetotalerrorofthemachine[1].
Thespindleisoneoftheimportantcomponentsofthemachine,anditsperformanceaffectstheoveralllevelofthemachinedirectly.
Whenthemechanicalspindleisworking,theinternalheatsourceofthespindlecomesformtheheatgeneratedbythefrictionofhigh-speedrotation'sbearing.
Whenthetemperaturehasrisen,therelativespatialpositionandsizeofthespindleandotherpartsofthemachinewillbedifferentfromtheprevioustemperature.
Itwillformadifferenttemperaturefieldandproducedifferentdegreesofthermaldeformation[2].
Therefore,thethermalcharacteristicsofresearchandanalysisonthespindlesystemiscrucialtoensuretheaccuracyofthemachine.
Itisoneofthekeytechnologiestobeconsideredinhighprecisionmachinetools.
Thethermalcharacteristicsanalysisofthespindlesystemistostudythedistributionofthetemperaturefield.
Atpresent,therearemanyscholarswhostudythethermalcharacteristicsofmachinetoolspindlesystemathomeandabroad.
Forexample,JinKyungChoiofSouthKoreastudiedthermalcharacteristicsforthespindleandbearingsystemwiththefiniteelementmethod[3].
M.
H.
AttiafromCanadaanalyzedthewholetemperaturefieldofthemachineusingthefiniteelementmethod[4].
CeGuoandQinghongSunfromSoutheastUniversityhavealreadyestablishedafiniteelementmodelofthehigh-speedprecisionlathespindlecomponents'temperaturefield[5].
YouweiHongestablishedthefiniteelementmodelofthegantrymachiningcenterandsimulatedthetemperaturefielddistributionandvariation[6].
ThearticleisbasedonCNClatheprecisionspindlesystemofthe170CP06astheresearchobject.
Thetemperaturefieldmodelofthemechanicalspindleisestablishedanditisconductedthesteady-stateandtransientthermalanalysisofthespindlesystem.
Thetemperaturefieldofspindlesystemisinvestigatedtogetthetemperaturefielddistributionandthermalbalancetimeofthespindlesystem.
Thethermalexperimentswithoutloadarecarriedoutinordertoverifythereliabilityofthemodel.
CalculationofthethermalparametersTheheatsourceisthefoundationofthespindletemperaturefieldresearch.
Theheatsourceofthespindlesystemincludescuttingheatandbearingfrictionheat.
Thecuttingheatinthemachiningprocessistakenawaybycoolantliquidandswarf.
Therefore,theheatsourceofthespindlemaybemainlythebearingfrictionalheat.
CalculationofthecalorificvalueTherollingbearing'sheatismainlygeneratedbythebearingfrictionaltorque.
Theformulais41.
04710fHnM=*(1)Intheformula,Hfisthecalorificvalueofthebearing;nisthespindlespeed;M0isthebearingfrictionaltorque.
Thebearingfrictionaltorqueisthesumofthebearingrollingfriction,slidingfrictionandlubricantfrictionwhichhavegeneratedtoblockthebearingrunningtorque.
Palmgren[7]deducedtheempiricalformulawhichcalculatesthebearingfrictiontorque.
Thebearingfrictionaltorqueiscalculatedas01MMM=+(2)Intheformula,M0isrelatedtotheviscosityofthelubricant.
M1isrelatedtotheloadofthebearingregardlessofspeed.
ItonlyconsidersM0withoutload.
Palmgrenconfirmedtheexpressionusingempiricalmethods:72/3300=10()mMfnDν2000nν≥(3)730016010mMfD=*2000nν<(4)Intheformula,νisthekinematicviscosityofthelubricantinthebearingoperatingtemperature,mm2/s;0fisthecoefficientrelatedtothebearingtypesandlubrication,mDistheaveragediameterofthebearing,mm,0.
5()mDDd=+.
Whenthespindlesystemisanalyzed,thethermalloadisloadedbythewayofbearingtheheatrate.
Theformulais[9]3(/)fHqWmV=(5)Intheformula,Visthevolumeoftheheatsource;22)2/(bmDDVπ=,andDbisthediameteroftherollingelements.
Calculatedbytheequation(1)to(5),whenthespindlespeedis2000r/min,wecangettheheatratesoftheforeandrearbearingtobe342704.
4W/m3and348161.
76W/m3.
CalculationoftheheattransfercoefficientAccordingtotheheattransfertheory[10],wecanknowtheheattransferwayaretheheatconduction,theconvectionandthethermalradiation,thelossoftheradiationheatislessforthespindlesystem.
Whenweareanalyzingthetemperaturefieldofthespindlesystemonlytoconsiderthethermalconductionandtheconvectionheattransfer.
Thethermalconductivitydependsonthethermalconductivityofthecomponentsinthespindlesystem.
Theconvectiveheattransferistheconvectionofthespindlesurfaceandtheair.
Theconvectiveheattransferisformedbydrivingtherotationofthespindlearoundtheairbetweenthecaseandthespindle.
ThecoefficientoftheheattransferdependsonthecriterionofNusselt[12].
/cchNlλ=(6)Intheformula,chisthecoefficientoftheheattransfer;λisthethermalconductivityoftheair;NisthecoefficientofNusselt;clisthefeaturesize.
TheNusseltformulaoftheforcedconvectionis23130.
133RePrN=5Re4.
3100.
7Pr670)<*<<(,(7)AccordingtoReynoldsCriterion,wecanknowRe=/cculν(8)Intheformula,ReistheReynoldsnumber;PristhePrandtlnumberofthefluid;cuistheaveragevelocityoftheair;νisthecoefficientoftheair'smotionviscosity.
Whenthespindlerotatesbyhighspeed,theaveragevelocityoftheairis[13]=/60cudnπ(9)1122=nndldldldl++(10)12nllll11)Intheformula,distheaveragediameterofthespindle;nisthespeedofthespindle.
Calculatedbytheequation(6)to(11),whenthespindlespeedis2000r/min,wegeteachheattransfercoefficientswhichare26.
62/()Wmk,35.
632/()Wmk,38.
32/()Wmk,32.
52/()Wmk,35.
22/()Wmk.
FiniteelementmodelofthespindlesystemTheprecisionspindlesystemofthe170CP06ismainlycomposedofthespindle,case,beltpulley,bearingcoverandtheangularcontactballbearings,etc.
Themotordrivesbyabeltpulleymountedontheshafttoprovideadrivingforceforthespindle.
Themainparametersofthespindleis:ItsmaterialisalloySteel.
Thetotallengthis497mm.
Themaximumdiameterofthespindleismm100φ.
Theratedspeedofthespindlesystemis4500r/min.
Themaximumpoweris35kWandthemaximumtorqueis180N.
m.
Fig.
1isthestructurediagramforspindlesystem.
1—Bignut2—Beltpulley3—Leftcover4—Case5—Rightcover6—Spindle7—Forebearing8—RearbearingFig.
1StructurediagramforspindlesystemThemodelofthespindlesystemisestablishedbyusingthethree-dimensionalmappingsoftware—SoildWorks.
Anditsimplifiesappropriatelythestructurethatinfluencesanalysisresultsless.
Accordingtothespindleoftheboundaryconditionsandheattransfercharacteristics,Simplifiedsolidmodelisintroducedtothefiniteelementanalysissoftwaretobemeshingofthegrid[12].
Fig.
2isasimplifiedandmeshingmodelofthespindlesystem.
Theentiremodelhas128,143unitsand232,855nodes.
Fig.
2MeshingofthespindlesystemSimulationanalysisofthespindlesystem'stemperaturefieldThethermalanalysisisestablishedinthesoftwareoffiniteelementanalysis.
Thematerialofthespindleandbearingaredefinedasalloysteel.
Theambienttemperatureis26C°.
Accordingtotheboundaryconditionsofthespindleandthecharacteristicsoftheheattransfer,theheatgenerationrateoftheforeandrearbearingsis342704.
4W/m3and348161.
76W/m3whichareappliedtotheforeandrearbearings.
Thecoefficientsoftheheattransferconvectionareaddedtotherespectivemembersurfacespindlesystemasboundaryconditions.
Itisconductedthesteady-stateandtransientthermalanalysisofthespindlesystem.
TheanalysisofthesteadytemperaturefieldWhenthespindlespeedis2000r/min,wecangetthesimulationofthesteady-statetemperaturefieldresultinginthesteady-statetemperaturefieldcontourofthespindlesystem.
AsisshowninFig.
3.
Fig.
3Steady-statetemperaturedistributionofspindlesystemFig.
3showsthatthemaximumtemperatureofthespindlesystemappearsattheinnerringoftherearbearing.
Itstemperatureis38.
5C°.
Themaximumtemperatureriseis12.
5C°.
Theheatoftherearbearingislargerthantheforebearing.
Anditiscausedbythepoorcoolingconditionoftheinnerring.
TheanalysisofthetransienttemperaturefieldWhenthespindlesystemistheanalysisofthetransienttemperaturefieldtogetthebearingtemperaturecurveandthethermalequilibriumtimebysettingtheoperatingtimeof65min.
Fig.
4arethecontoursofthetemperaturefieldatdifferenttimepoints.
1600s2400s3200s3600sFig.
4ContoursofthetemperaturefieldatdifferenttimepointsThespindlesystemhasreachedthethermalequilibriumafterrunning60min.
Thehighesttemperaturesoftheforebearingandrearbearingare34.
19C°and35.
9C°.
ExperimentaltestTheautomatictestsystemofmechanicalspindlecharacteristicisusedforthetemperaturerisetestwhichisinthestatusoftheofmechanicalspindletorqueoutput,theloadandwithoutloadateachspeed.
Thetestsystemconsistsofthemachinebase,torqueandspeedsensors,industrialcomputer,ervomotor,multi-channeltemperaturecontrolinstrumentandsoon.
Thetestprincipleisthatthespindleconnectsthearresterdetentviacouplings,torqueandspeedsensorandthemotordrivesbyabeltdrivetomakethespindlerotatebychangingthebrakeexcitationcurrentmethodtotheloadcontrolforthespindlesystem.
Fig.
5istheoperatingprincipleoftheexperimentplatform.
Fig.
6istheexperimentdeviceofmechanicalspindlesystem.
Fig.
5OperatingprincipleoftheexperimentplatformFig.
6TheexperimentdeviceofmechanicalspindlesystemThetemperaturesensorsaredisposedwithintheouterringoftheforeandrearbearings,therearendsurfaceoftherearbearingandandoutersurfaceofthecase.
Fig.
7isthedistributionoftestpoints.
Atthespeedof2000r/minand4500r/min,thespindlesystemistestingtemperaturerisethewithoutload.
Whenthespindlesystemhasreachedtheequilibrium,wecanmeasurethetemperatureofeachofthekeyparts.
Wewilltaketestpoint2andtestpoint8forexampleandcanseethechangesinthebearingtemperaturewithtime.
Fig.
8isthetemperaturerisecurvefortestpoint2and8atthespeedof2000r/minand4500r/min.
123456789111210Fig.
7Thedistributionoftestpoints05101520253035404550556065202224262830323436T/°Ct/minSimulationvalueExperimentalvalue05101520253035404550556065202224262830323436T/°Ct/minSimulationvalueExperimentalvaluea.
Thetemperatureoftestpoint2(Speedof2000r/min)b.
Thetemperatureoftestpoint8(Speedof2000r/min)051015202530354045505560652022242628303234363840424446T/℃t/minSimulationvalueExperimentalvalue0510152025303540455055606520222426283032343638404244T/℃t/minSimulationvalueExperimentalvaluec.
Thetemperatureoftestpoint2(Speedof4500r/min)d.
Thetemperatureoftestpoint8(Speedof4500r/min)Fig.
8Temperaturerisecurvefortestpoint2and8(Speedof2000r/minand4500r/min)AscanbeseenfromFig.
8,wecanseethattherearesomeerrorscomparedwithexperimentaldataandsimulationdata.
Butthereisthesameupwardtrendbasicallythatexplainsthemodelisreliable.
Whenthespindlespeedis2000r/minandthesystemhasbeenrunningfor60mins,thesystemhasreachedsteadystatetemperature.
Andthehighesttemperaturesoftestpoint2and8are34.
19C°and35.
9C°.
Therearemoreobviouschangesofthetemperaturerisewhenthespindlesystemisrunningatthebeginning.
Thetemperaturerisechangessmallerafter55minandreachessteadystateabout57.
5min.
Whenthespindlespeedis4500r/min,thespindlesystemrisesfasterbefore52.
5minandreachesequilibriumabout55min.
Next,wewilltestthetemperaturerisewhenthespindlespeedare1000r/min,1500r/min,2500r/min,3000r/min,3500r/minand4000r/min.
Asthekeypartsofthetestpoints2and8forexample,WecanobtainthemaximumtemperatureofeachtestpointunderdifferentspeedsasshowninFig.
9.
05001000150020002500300035004000450026283032343638404244T/℃Speed(r/min)Testpoint2Testpoint8Fig.
9SpindletemperatureatdifferentspeedsAscanbeseenfromFig.
9,asthespindlespeedincreases,thetemperatureriseofthebearingsismoreandmorehigher.
Andthetestpoint2isslightlyhigherthanthetestpoint8.
Whenthespindlespeedchanges1000to3000r/min,thebearingtemperaturechangesmoreobviously.
Thechangeofthetemperatureisflatrelativelywhenthespindlespeedchanges3000to4500r/min.
ConclusionInthispaper,itisconductedthethermalanalysisofthespindlesystemcombiningthemethodofthefiniteelementanalysiswithexperimentalverificationandresultinginthefollowingconclusions:(1)Theaboveanalysisshowsthatthesimulationmodelofthemachinespindleisreliable.
Theresultoferrorsislessthan3%comparedthesimulationdatawiththeexperimentaldata.
(2)Whenthespindlespeedischanging1000to3000r/min,thetemperatureofbearingshavechangedmoreobviously.
Thechangeofthetemperatureisflatrelativelywhenspindlespeedischanging3000to4500r/min.
Itindicatesthatthespeedimpactsthetemperaturegreaterunderlowspeeds.
Andforthehighspeed,thetemperatureisimpacttothespeedrelativelysmall.
Forthespindle,whichistheratedspeedof4500r/min,thetemperaturechangesrapidlyunderitstwo-thirds'ratedspeed.
Whilethespeedismorethantwo-thirds'ratedspeed,thetemperaturechangesslowly.
(3)Thespindlesystemhasreachedthedifferentthermalequilibriumtimeatdifferentspindlespeeds.
Thehigherthespeedis,theshorterthespindlehasreachedthermalequilibriumtime.
(4)Theprecisionspindleof170CP06hasreachedthethermalequilibriumatratedspeedfor55min.
Thehighesttemperatureis45.
2C°thatoccurstothebearbearing.
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