文献翻译一种新型并联机床的尺寸公差分配.docx
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文献翻译一种新型并联机床的尺寸公差分配.docx
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文献翻译一种新型并联机床的尺寸公差分配
DimensionalToleranceAllocationforNewTypeofParallelMachineTools
1INTRODUCTIONS
Theprototypeofanewtypeofparallelmachinetoolsisa6-6Stewartplatformmechanism.Comparedtothetraditionalmachinetool,aparallelmachinetoolpossessesmanyadvantages,suchashighprecision,highstructuralrigidityandhighmachiningforce/torquecapacity,etc.Currently,manyuniversitieshaveresearchonthiskindofmachinetools.AsshowninFig.1,theparallelmachinetoolcomprisesthefollowingfourparts:
afixedplatform,sixin-parallelactuators,thelengthvariationofeachactuatorisimplementedbyball-screwsandtheball-screwsaredrivenbyservomotors.Theballjointsconnectthefixedandmovingplatformswithball-screws;aspindleisinstalledonmovingplatformbottom.Whenmachiningworkisbeingcarriedoutthevariationofthemovingplatformallowsaparallelmachinetooltomachinecomplicatedcurvedworkpiecesuchasdie,impelleretc.
ThedevelopingtendencyofmodernNCmachinetoolsishighspeedandhighprecision,andthemachinetoolerrorshavedirecteffectonmachinetoolprecision.Inordertomeettheprecisionspecified,ascientificdimensionaltoleranceallocationisurgentlyrequiredinthedesignofthiskindofmachinetool.Theerrorsofthemachinetoolincludethefollowingparts:
1)transmissionerrorintransmissionchains,i.e.,pitchcumulativeerroroftheball-screwineachactuatoranddeaddomainerrorduringstartingorreversingoperation;2)lengthtransformerroroftheball-screwduetotheinfluenceofambienttemperature;3)paresclearanceerrorthatconnectfixedandmovingplatform;4)othererrors,i.e.,positioningerrorcausedbytransmissionrigidity,dynamicerrorcausedbymovingpartsmassandvelocitydamping.Theaboveerrorswillfinallyleadtoerroratthecutterheadofthemachinetool.Thispaperwillcarryoutresearchondimensionaltoleranceallocationbasedonakindofstatisticalexperimentmethod,Monte-Carlomethod.
2SOLUTIONOFINVERSEKINEMATICSFORMACHINETOOL
Thekinematicssolutionforthisparallelmachinetoolcanbeclassifiedintotwotypes.Whentheknownquantityisthelengthsofthesixactuatorsandtheorientationofthecutterhead,thisiscalleddirectkinematics;Onthecontrary,whentheknownquantityisthepositionandtheorientationofthecutterheadandtheunknownquantityisthelengthsofthesixactuators,thisiscalledinversekinematics.Thesolutionofthedirectkinematicsofthemachinetoolisusedtomonitorwhilethesolutionoftheinversekinematicsofthemachinetoolisusedtocontrol.AsshowninFig.2,afixedcoordinateframeO-XYZisattachedtothefixedplatformandamovingcoordinateframeO’-X’Y’Z’isattachedtothemovingplatform.Thecenterofthejointconnectingtheitchactuatortothefixedplatformwillbedenotedas
whereasthecenterofthejointconnectingthesamelegtothemovingplatformwillbedenotedas
theY-axisofthefixedcoordinateframeisselectedalongthelinewhichbisectstheangle
andtheY’-axisofthemovingcoordinateframeisselectedalongthelinewhichbisectstheangle
.LetthepositionofpointO’withrespecttotheoriginofthefixedcoordinateframebedenotedbyvector
vectors
willbedefinedasthepositionvectorsofthemovingcoordinateframe,thuswecanwritethepositionvectorsofthemovingplatformjointsinfixedcoordinateframeas:
Wherematrix
istherotationmatrixdescribingtheorientationofthemovingplatformwithrespecttothefixedplatform,theelementsofmatrix
areshownbyRPYexpression.Let
beanglesthatthemovingplatformrotatesaboutX-axis,Y-axis,Z-axisofthefixedcoordinateframe,andthenwecanobtain:
Letvectors
bethepositionvectorsoftheplatformjointswithrespecttothefixedcoordinateframe,thenthelengthofeachactuatorcanbewrittenas:
3DIMENSIONALTOLERANCEALLOCATIONSWITHMONTE-CARLOMETHOD
2.1DeterminationofTotalDimensionalChainErroroftheMachineToolLinks
Inordertocarryoutdimensiontoleranceallocation,thevariationfeaturebetweentheerrorsofthein-parallellinksandorientationerrorofthecutterhead(orthecenterpointofthemovingplatform)needtoknow.Thedirectkinematicsisusedtoderivethecutterheaderrorfromthelinkerrorsofthemachinetool.Itisdifficulttoobtainanalyticalsolutionbydirectkinematics.Soaninverseerrorestimationmethodbywhichthelinkerrorscanbederivedfromthepositionandorientationerrorsofthecutterheadisadopted.
Thekeytothedimensionaltoleranceallocationistodeterminethetotaldimensionalchainerrorofthemachinetoollinks.Monte-Carlomethodisanumeralmethodtosolvemathematicsbasedonrandomsampling.Inthisparallelanevenly-distributedMonte-Carlorandomsimulationmethodon
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- 文献 翻译 一种 新型 并联 机床 尺寸 公差 分配
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