推板式造波机的机械结构设计（全套含CAD图纸）
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上传时间：2018-01-08
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板式
造波机
机械
结构设计
全套
cad
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PREPRINTSERIESISSUENO200919STUTTGARTRESEARCHCENTREFORSIMULATIONTECHNOLOGYSRCSIMTECHSIMTECHCLUSTEROFEXCELLENCEPFAFFENWALDRING7A70569STUTTGARTPUBLICATIONSSIMTECHUNISTUTTGARTDEWWWSIMTECHUNISTUTTGARTDESFREYAADADALAUAAVERLAEXPEDIENTMODELINGOFBALLSCREWFEEDDRIVESSTUTTGART,FEBRUARY2011AINSTITUTEFORCONTROLENGINEERINGOFMACHINETOOLSANDMANUFACTURINGUNITSISW,UNIVERSITYOFSTUTTGART,SEIDENSTRAE36,70174STUTTGART/GERMANYALEXANDRUDADALAUISWUNISTUTTGARTDEWWWISWUNISTUTTGARTDEABSTRACTBALLSCREWFEEDDRIVESARETHEMOSTCOMMONLYUSEDMECHANISMTOPROVIDELINEARMOTIONINHIGHSPEEDMACHINETOOLSPOSITIONACCURACYANDTHEACHIEVABLECLOSEDLOOPBANDWIDTHOFSUCHDRIVESYSTEMSAREUSUALLYLIMITEDBYTHESTRUCTURALVIBRATIONMODESOFTHEMECHANICALCOMPONENTSHIGHERORDERPLANTMODELSALLOWFORABETTERUNDERSTANDINGOFTHESYSTEMDYNAMICS,IMPROVETHEDESIGNPROCESSOFFEEDDRIVESANDAREESSENTIALFORTHEDEVELOPMENTOFSOPHISTICATEDCONTROLSTRATEGIESTHISWORKPRESENTSACLEARLYARRANGEDANDVERSATILEMODEL,CAPABLEOFEXPRESSINGTHERELEVANTDYNAMICSOFBALLSCREWFEEDDRIVESKEYWORDSMACHINETOOLSIMULATIONBALLSCREWPLASTICITYINTRODUCTIONDYNAMICALFEEDDRIVESCOMMONLYUSEDINMACHINETOOLSANDPRODUCTIONUNITSREPRESENTCOMPLEXMECHANICALSTRUCTURESWITHMULTIPLEDEGREESOFFREEDOMDOFANDVARIOUSEIGENMODESNUMEROUSSCIENTIFICWORKSHAVEDEALTWITHTHESIMULATIONOFSUCHDRIVESYSTEMS,USINGFINITEELEMENTMETHODSFEMANDCOMPLEXMODELINGTECHNIQUESINORDERREPRESENTTHEDYNAMICALBEHAVIORASDETAILEDASPOSSIBLE13INCONTRARYTHEAPPROACHPRESENTEDINTHISPAPERAIMSATFINDINGANINTUITIVEANDEASYTOUSEMODEL,CAPABLEOFEXPRESSINGTHEMOSTRELEVANTCHARACTERISTICSOFABALLSCREWFEEDDRIVEWITHRESPECTTOTHEIRAPPLICATIONINMACHINETOOLSGENERALLYSPOKENABALLSCREWDRIVECANBECHARACTERIZEDASASYSTEMWITHTHREEDIFFERENTTYPESOFEIGENMODESAXIAL,ROTATIONALANDFLEXURALMODES4TYPICALLYTHEFIRSTAXIALANDROTATIONALMODEOFTHEBALLSCREWSHOWADOMINANTINFLUENCEONTHEOVERALLDYNAMICSWHILETHERELEVANCEOFHIGHERORDERMODESFORMOSTTECHNICALAPPLICATIONSISRATHERSMALLTHEEXCITATIONOFTHEFLEXURALMODESANDTHEIREFFECTONTHEFEEDMOTIONGREATLYDEPENDONFABRICATIONANDMOUNTINGTOLERANCESASWELLASONTHEOPERATINGCONDITIONSOFTHEDRIVESYSTEMPRESUMINGPROPERMOUNTINGANDOPERATINGCONDITIONS,THEEXCITATIONOFTHEFLEXURALMODESARECONSIDERABLYSMALLANDTHEREFOREWILLBENEGLECTEDINTHECOURSEOFTHISPAPERTHETWODOMINANTVIBRATIONALDEGREESOFFREEDOM,NAMELYTHEAXIALANDROTATIONALMODE,AREPRIMARILYINFLUENCEDBYTHEGEOMETRICALDIMENSIONSANDTHEPITCHOFTHEBALLSCREWSHAFTDEPENDINGONTHETRANSMISSIONRATIOASWELLASONTHEOPERATINGCONDITIONSTHESYSTEMCANBEHAVEQUALITATIVELYANDQUANTITATIVELYVERYDIFFERENTINMOSTCASESHOWEVER,THECONFIGURATIONOFAFEEDDRIVEALLOWSFORASIMPLEAPPROXIMATIONOFTHESYSTEMSCHARACTERISTICSINTHEFOLLOWINGAPRACTICALANDAPPLICATIONORIENTEDMODELINGTECHNIQUEFORBALLSCREWFEEDDRIVESWILLBEDERIVEDANDVERIFIEDBYMEASUREMENTRESULTSBALLSCREWFEEDDRIVESFORMACHINETOOLSFIGURE1SHOWSATYPICALBALLSCREWASSEMBLYWITHITSRELEVANTCOMPONENTSINTHISCASESERVOMOTORANDBEARINGSAREFIXEDTOTHEMACHINEBASEANDTHETORQUEOFTHESERVOMOTORISTRANSMITTEDTHROUGHANELASTICCOUPLINGONTOTHEBALLSCREWSHAFTNOTDEPICTEDINFIGURE1ARETHELINEARGUIDEWAYSCONSTRAININGTHEMOVEMENTOFTHEMACHINETABLEINAXIALDIRECTIONTHETRANSFORMATIONFROMTHEROTATIONALINTOTHELINEARMOTIONISREALIZEDBYTHEBALLSCREWSYSTEMWITHITSTRANSMISSIONRATIOI,DEFINEDASTHEDISTANCEOFTRAVELHDURINGONEREVOLUTIONOFTHESHAFT1MANUFACTURERSPROVIDEAGREATVARIETYOFBALLSCREWSYSTEMSWITHDIFFERENTCONSTRUCTIVEDESIGNS,DIMENSIONSANDTRANSMISSIONRATIOSTHEAVAILABLEPITCHESNOWADAYSLIEBETWEEN005AND3TIMESTHEBALLSCREWDIAMETER,WHILEFORMOSTAPPLICATIONSINMACHINETOOLSVALUESBETWEEN025AND1AREBEINGUSEDFIG1SCHEMATICCONFIGURATIONOFABALLSCREWFEEDDRIVETHEDYNAMICALBEHAVIOROFSUCHADRIVESYSTEMISGREATLYINFLUENCEDBYTHEPHYSICALDIMENSIONSOFTHEBALLSCREWSHAFTDIAMETERANDLENGTHOFTHESHAFTHAVEADECISIVEIMPACTONTHEOVERALLRIGIDITYANDTHEREFOREONTHEDYNAMICALBEHAVIOROFTHEDRIVESYSTEMFIGURE2SHOWSAMEASUREDFREQUENCYRESPONSEOFABALLSCREWDRIVE,DERIVEDFROMTHECOMPARISONOFMOTORANDMACHINETABLEVELOCITYFIG2MEASUREDFREQUENCYRESPONSEOFABALLSCREWFEEDDRIVECLEARLYNOTICEABLEARETHETWODOMINANTEIGENFREQUENCIESF1ANDF2,CHARACTERISTICALFORBALLSCREWFEEDDRIVESTHEFIRSTEIGENFREQUENCYINFIGURE2REPRESENTSANAXIALOSCILLATIONOFTHEMACHINETABLEWHILETHESECONDEIGENFREQUENCYCANBEPRIMARILYASCRIBEDTOANANGULARDEFLECTIONOFTHEROTATIONALSYSTEMALTHOUGHEACHMODEISARESULTOFAXIALANDANGULARDEFORMATIONS,ITISCONVENIENTTOCLASSIFYANAXIALANDAROTATIONALMODEDEPENDINGONTHEPREDOMINANTDEFORMATIONINBOTHCASESTHEFLEXIBILITYOFTHEBALLSCREWSHAFTHASAMAJORINFLUENCEONTHEABSOLUTEVALUEOFTHEEIGENFREQUENCIESTHISISDUETOTHEFACTTHATTHESHAFTREPRESENTSTHECOMPONENTWITHTHELEASTRIGIDITYWITHINTHEDRIVESYSTEM5FURTHERMORETHEPROPERTIESOFTHEBALLSCREWSHAFTARENOTCONSTANTBUTCHANGEOVERTHETRAVELRANGEOFTHEMACHINETABLEATTHISPOINTITSHOULDBENOTEDTHATFORMOSTTECHNICALAPPLICATIONSTHEEIGENFREQUENCYOFTHEAXIALMODEISARTICULATELYSMALLERTHANTHATOFTHEROTATIONALMODEONTHISACCOUNTTHEAXIALMODEISOFTENREFERREDTOASTHEFIRSTEIGENFREQUENCYOFABALLSCREWFEEDDRIVETHESTRUCTURALVIBRATIONMODESOFTHEMECHANICALSYSTEMAREOFPARTICULARIMPORTANCEWHENCONSIDERINGTHEDYNAMICALBEHAVIOROFAPOSITIONCONTROLLEDFEEDDRIVEESPECIALLYINHIGHSPEEDAPPLICATIONS,HIGHACCELERATIONANDJERKVALUESCANEXCITETHEMECHANICALSTRUCTUREANDTHEREFOREHAVETOBECONSIDEREDWHENTUNINGTHECONTROLLERWHENUSINGCASCADEDPPOSITIONPIVELOCITYCONTROLLER,THECLOSEDLOOPBANDWIDTHANDTRACKINGACCURACYOFTHEFEEDDRIVEISDIRECTLYLIMITEDBYTHEFIRSTEIGENFREQUENCYOFTHEMECHANICALSYSTEM6,7INSIMILARMATTEREXTERNALEXCITATIONSEGCUTTINGFORCESCANCAUSEUNWANTEDOSCILLATIONSANDSTABILITYPROBLEMSMORESOPHISTICATEDCONTROLSTRATEGIESUSINGPLANTMODELSINTENDTOCOMPENSATETHESENEGATIVEEFFECTS,REQUIRINGDETAILEDINFORMATIONANDAGOODUNDERSTANDINGOFTHEMECHANICALSYSTEM8,9THEDEMANDFOREVENHIGHERDYNAMICSANDBETTERTRACKINGACCURACYINMACHINETOOLSTHEREFOREGOESALONGWITHHIGHLYEFFICIENTANDACCURATEFEEDDRIVEMODELSCOMPARISONOFTWODIFFERENTMODELINGTECHNIQUESINORDERTOEXAMINETHEINFLUENCEOFTHESHAFTONTHEOVERALLDYNAMICALBEHAVIOROFABALLSCREWDRIVE,TWOSIMPLIFIEDMODELSWITHDIFFERENTDEGREESOFCOMPLEXITYAREBEINGINTRODUCEDANDCOMPAREDTOONEOTHERTHEFIRSTMODELISBUILTUPINFEMUSINGACOMBINATIONOFSPRINGS,DAMPERS,MASSELEMENTSANDTIMOSHENKOBEAMELEMENTSWECALLTHISMODELAHYBRIDMODELSINCEWEAREUSINGDISCRETEANDCONTINUOUSFORMULATIONELEMENTSTHERELEVANTAXIALANDROTATIONALFLEXIBILITIESOFTHESYSTEM,NAMELYTHEAXIALRIGIDITYOFTHEFIXEDBEARINGINCLUDINGTHEMOUNTINGKBEARING,THERIGIDITYOFTHEBALLSCREWNUTKNUTANDTHETORSIONALRIGIDITYOFTHECOUPLINGKCOUPLINGAREBEINGEXPRESSEDASLINEARSPRINGSTHEINDIVIDUALDAMPINGVALUESARETREATEDINEQUALMEASURETHESHAFTINCLUDINGBOTH,RELEVANTAXIALANDTORSIONALCHARACTERISTICS,ISMODELEDWITHTIMOSHENKOBEAMELEMENTSANDCOUPLEDWITHTHESURROUNDINGSPRINGSANDDAMPERSTHISPROVIDESTHEPOSSIBILITYOFANEXACTEXAMINATIONOFTHESTRUCTURALBEHAVIOROFTHESHAFTANDITSINFLUENCEONTHEOVERALLDYNAMICALBEHAVIORINCONCORDANCETOTHEREALMECHANICALSYSTEM,ROTATIONALANDAXIALMOTIONARECOUPLEDBYTHETRANSMISSIONRATIOI,WHICHISMODELEDUSINGCONSTRAINTEQUATIONSONTHEINVOLVEDDOFFIGURE3DEPICTSTHECOMPOSITIONOFTHISHYBRIDMODELX2KROTCROT1KAXCAXMTKNUTCNUTX1X32JMIH/2TIMOSHENKOBEAMELEMENTTABLEPOSITIONX2FIG3HYBRIDMODELOFABALLSCREWDRIVETHESECONDMODEL,ENTIRELYUSINGLUMPEDPHYSICALFEATURES,ISREFERREDTOASADISCRETEMODELDUETOITSSIMPLICITYITCANBEDIRECTLYMODELEDWITHCACETOOLSCOMPUTERAIDEDCONTROLENGINEERINGTOOLS,USINGAVAILABLESTANDARDBLOCKSLIKEGAINS,INTEGRATORSANDBASICMATHEMATICALOPERATIONSINTHISCASETHECHARACTERISTICSOFTHESHAFTARESEPARATEDINTOTWODIFFERENTBRANCHES,ANAXIALANDAROTATIONALBRANCHSINCEALLCOMPONENTSAREEXPRESSEDBYDISCRETESPRINGSANDDAMPERS,THERIGIDITYVALUESOFSHAFT,COUPLINGANDBEARINGARECOMBINEDTOANOVERALLAXIALKAXANDROTATIONALVALUEKROT23FIGURE4SHOWSTHEPRINCIPLESETUPOFTHEDISCRETEMODELTHEINDIVIDUALPARAMETERSINEACHMODELSUCHASTHEMASSOFTHEMACHINETABLE,THEMASSOFTHEBALLSCREWSHAFT,THEROTARYINERTIAOFSHAFTANDMOTOR,ASWELLASTHERIGIDITYANDDAMPINGFACTORSCORRESPONDTOTHEIRPHYSICALVALUESJSX2KROTCROT1MSKAXCAXMTKNUTCNUTX1X32JMIH/2FIG4DISCRETEMODELOFABALLSCREWFEEDDRIVEPRECONDITIONFORTHISAPPROACHISTHEDEFINITIONOFADEQUATE,ALTERNATIVEVALUESFORTHEAXIALANDROTATIONALRIGIDITYOFTHESHAFTFORTHISPURPOSETHESHAFTISCONSIDEREDASASOLIDSTEELRODYOUNGMODULUS,SHEARMODULUS,DENSITYWITHTHEDIMENSIONSOFTHEBALLSCREW,NAMELYEQUIVALENTDIAMETER,LENGTHANDEFFECTIVELENGTH,THEAXIALANDROTATIONALRIGIDITYVALUESOFTHESHAFTANDCANBEAPPROXIMATEDUSINGEQUATIONS4THROUGH6456NOTICETHATTHEALTERNATIVEROTATIONALRIGIDITYOFTHESHAFTHASBEENAPPROXIMATEDUSINGTHEEIGENFREQUENCYOFASOLID,ONONESIDEFIXEDRODWHICHCANACCORDINGTO10BECALCULATEDUSINGEQUATION6WITHTHISAPPROACHTHEAXIALRIGIDITYOFTHESHAFTDEPENDSONTHEEFFECTIVELENGTHLEFFWHILETHEROTATIONALRIGIDITYISCONSIDEREDCONSTANTTHROUGHOUTTHETRAVELRANGEOFTHEMACHINETABLEINTHEFOLLOWINGBOTHMODELSHAVEBEENEXAMINEDWITHANIDENTICALSETOFPARAMETERSACCORDINGTOTABLE1TABLE1PARAMETERVALUESUSEDFORTHESIMULATIONSROTARYINERTIAMOTOR640E03KGM2ROTARYINERTIACOUPLING650E04KGM2AXIALRIGIDITYNUT50000N/MTORSIONALRIGIDITYCOUPLING14100NM/MRADBALLSCREWDIAMETER3800MMLENGTHSHAFT200000MMAXIALRIGIDITYBEARING250N/MFURTHERISSHOULDBENOTICEDTHATTHEEXACTEQUIVALENTDIAMETERDEPENDSONALLGEOMETRICPARAMETERSOFTHEBALLSCREW,INCLUDINGSCREWPITCHIN11ITISSHOWN,THATSPINDLEPITCHCANAFFECTTHEAXIALANDTORSIONALSTIFFNESSOFBALLSCREWSUPTO15FORREASONSOFSIMPLICITYINTHISWORKTHEBALLSCREWDIAMETERISCHOOSENTOBECONSTANTTHESIMULATIONRESULTS,NAMELYTHEFIRSTTWOEIGENFREQUENCIESOFTHEFEEDDRIVE,AREPRESENTEDINTABLE2TABLEMASSSCREWPITCHTABLEPOSITION1STEIGENFREQUENCYHZ2NDEIGENFREQUENCYHZKGMMMMHYBRIDMODELDISCRETEMODELPERCENTALDIFFERENCEHYBRIDMODELDISCRETEMODELPERCENTALDIFFERENCE3001050010121008043754345081300101000907904033757344284300101500831827043759343886300205009979861137663491733002010008888890037793463843002015008108150637873445903004050094491135380936324630040100082483411385335348330040150074277342387634681056001050072171903375434498160010100064764601375734428460010150059259100375934388660020500711704103765349073600201000633635023779346384600201500577583103786344490600405006736503438083629476004010005875951438523533836004015005285524638763468105TABLE2FIRSTTWOEIGENFREQUENCIESOFTHEBALLSCREWDRIVEMODELSFORDIFFERENTMASS,SCREWPITCHANDTABLEPOSITIONSASEXPECTEDTHEVALUEOFTHEFIRSTEIGENFREQUENCYGREATLYDEPENDSONTHEMASSANDTHEPOSITIONOFTHEMACHINETABLETHEHIGHERTHEMASSANDTHEGREATERTHEDISTANCEBETWEENMACHINETABLEANDFIXEDBEARINGTHESMALLERTHEVALUEOFTHEFIRSTEIGENFREQUENCYINCOMPARISONTOTHATTHESECONDEIGENFREQUENCYSEEMSTOCHANGERATHERINSIGNIFICANTLYWITHDIFFERENTOPERATINGCONDITIONSBOTHMODELSSHOWTHATTHEROTATIONALMODEREMAINSALMOSTCONSTANTFORAGREATRANGEOFPARAMETERSTHEDIFFERENCEBETWEENHYBRIDANDDISCRETEMODELEXPRESSEDINFIGURE5CANBEASCRIBEDTOTHESIMPLIFIEDREPRESENTATIONOFTHESHAFTINTHEDISCRETEMODELFIG5PERCENTALDIFFERENCEBETWEENHYBRIDANDDISCRETEMODELOFTHEBALLSCREWDRIVEFROMFIGURE5ITCANBESEENTHATTHEABSOLUTEDIFFERENCEASWELLASTHEPARAMETERSENSITIVITYOFTHEEIGENFREQUENCYGREATLYDEPENDSONTHEINTERACTIONBETWEENAXIALANDROTATIONALMODE,DETERMINEDBYTHETRANSMISSIONRATIOOFTHEBALLSCREWWITHINCREASINGTRANSMISSIONRATIOTHEINFLUENCEOFTHEROTATIONALRIGIDITYOFTHESHAFTONTHEOVERALLAXIALRIGIDITYINCREASESTHEPOSITIONDEPENDENT,EFFECTIVEAXIALRIGIDITYCANBEEXPRESSEDASFOLLOWS7INMANYCASESHOWEVER,THEINFLUENCEOFTHEROTATIONALRIGIDITYONTHEAXIALMODECANBENEGLECTEDDUETOTHETRANSMISSIONRATIOOFTHEBALLSCREWWITHTHEEFFECTIVEAXIALRIGIDITYANDTHEKNOWLEDGEOFTHECONSISTENCYOFTHEROTATIONALMODE,THETWOCHARACTERISTICEIGENFREQUENCIESOFABALLDRIVECANBEAPPROXIMATEDUSINGEQUATIONS8AND989DESPITETHECHOSENSIMPLIFICATIONSTHEDISCRETEMODELSHOWSGOODRESULTSFORTHEFIRSTTWOEIGENFREQUENCIESOFABALLSCREWSYSTEMTHISALLOWSFORANINTUITIVEANDCLEARLYARRANGEDSIMULATIONOFTHEDYNAMICALBEHAVIOR,VALIDFORAGREATRANGEOFPARAMETERSANDWELLSUITABLEFORMOSTPRACTICALAPPLICATIONSINTHEFOLLOWINGCHAPTERTHESIMULATIONRESULTSOFTHEDISCRETEMODELDEPICTEDINFIGURE4WILLBECOMPAREDTOMEASUREMENTSONANACTUALMACHINETOOLFEEDDRIVEEXPERIMENTALVERIFICATIONOFTHEMODELATTHEINSTITUTEFORCONTROLENGINEERINGOFMACHINETOOLSANDMANUFACTURINGUNITSISWATTHEUNIVERSITYOFSTUTTGARTEXISTSAGREATVARIETYOFTESTBENCHESWITHDIFFERENTSIZEBALLSCREWSANDNUMEROUSTRANSMISSIONRATIOSWHILETHERESEARCHONTHISTOPICISBASEDONEXPERIMENTSWITHDIFFERENTBALLSCREWTYPES,THEFOLLOWINGMEASUREMENTSFOCUSONATYPICALBALLSCREWSETUPFORMACHINETOOLSACCORDINGTOTHESPECIFICATIONSINTABLE3THEPARAMETERSUSEDFORTHESIMULATIONCOMPLYWITHTHOSEOFTHEEXPERIMENTALSETUPTHEVALUESFORRIGIDITYANDMASSAREBASEDONMANUFACTURERSDATAWHILETHEDAMPINGFACTORSCORRESPONDTOEMPIRICALVALUESTABLE3SPECIFICATIONSOFTHETESTBENCHWITHTHEGIVENFEEDDRIVEVARIOUSMEASUREMENTSHAVEBEENCONDUCTEDANDCOMPAREDTOTHESIMULATIONRESULTSFROMTHEDISCRETEMODELFIGURES6AND7EXEMPLARILYSHOWSIMULATEDANDMEASUREDFREQUENCYRESPONSESFORTHEGIVENFEEDDRIVEATDIFFERENTOPERATINGCONDITIONSFIG6SIMULATEDANDMEASUREDFREQUENCYRESPONSEFORTHEFEEDDRIVEATDIFFERENTMACHINETABLEPOSITIONSNOMINALDIAMETERBALLSCREWD040MMBALLSCREWLEADPH20MMDYNAMICALLOADVALUECN54600NNOMINALBALLDIAMETERDW6MMNUMBEROFBALLTRACKTURNS5TRAVELRANGE700MMMASSMACHINETABLE300600KGFIG7SIMULATEDANDMEASUREDFREQUENCYRESPONSEFORDIFFERENTMACHINETABLEMASSESTHEDISCRETEMODELUSEDTODESCRIBETHEMECHANICALSYSTEMSHOWSGOODCONCORDANCEWITHTHEBEHAVIOROFTHEACTUALFEEDDRIVEDESPITEOFTHECHOSENSIMPLIFICATIONSANDTHEIMPRECISENESSOFTHEMANUFACTURERSDATA,AGOODPREDICTABILITYCOULDBEACHIEVEDFURTHERMORETHEPREDICTEDPARAMETERDEPENDENCYOFTHEEIGENFREQUENCIESISCONFIRMEDBYTHEMEASUREMENTRESULTSTHEFREQUENCYOFTHEAXIALMODECHANGESDEPENDINGONMACHINETABLEMASSANDPOSITIONWHILETHEROTATIONALMODEOFTHEBALLSCREWDRIVEREMAINSALMOSTCONSTANTTHEINVARIANCEOFTHEROTATIONALMODETOWARDSOPERATINGCONDITIONS,ASALREADYDETECTEDINTHEFOREGOINGSIMULATIONS,CANBEEXPLAINEDBYTHELOWPASSCHARACTERISTICOFTHEMECHANICALSYSTEMAFTERTHEFIRSTEIGENFREQUENCYTHESYSTEMEXPERIENCESANAMPLITUDEDROPOFFOF20DB/DECADEHENCETHEENERGYIMPOSEDBYTHESERVODRIVEATHIGHERFREQUENCIESISMERELYTRANSFORMEDONTOTHEMACHINETABLETHEAXIALMOTIONOFTHETABLEATTHESECONDEIGENFREQUENCYISTHEREFOREQUITESMALLDUETOTHEKINEMATICCOUPLING,THEANGULARDEFLECTIONOFTHESHAFTWILLSTILLLEADTOANAXIALDISPLACEMENTWHICHINTHISCASEISPREDOMINANTLYEXECUTEDBYTHEDEFLECTIONOFTHESHAFT,BEARINGANDMOUNTINGCONSIDERINGTHEMINORCHANGESINTABLEPOSITIONATTHEROTATIONALMODEOFTHEBALLSCREWSYSTEM,ITISINTELLIGIBLETHATTHENEITHERTHEMASSNORTHEEFFECTIVEPOSITIONOFTHETABLEHAVEARELEVANTINFLUENCEONTHESECONDEIGENFREQUENCYOFTHEOSCILLATINGSYSTEMTHEPREDICTABILITYANDSIMULATIONOFTHEDOMINANTEIGENFREQUENCIESOFABALLSCREWDRIVEANDTHEIRDEPENDENCYTODIFFERENTOPERATINGCONDITIONSPROVIDESABETTERUNDERSTANDINGOFTHESYSTEMDYNAMICSANDISBENEFICIALFORTHEDESIGNPROCESSOFTHEMECHANICALCOMPONENTSASWELLASFORTHEIMPLEMENTATIONOFADEQUATEFEEDBACKCONTROLLERSINPARTICULARTHECONSISTENCYOFTHEROTATIONALEIGENMODEISQUITEFAVORABLEFORTHEDESIGNOFVIBRATIONREJECTIONANDCONTROLALGORITHMSSUCHASNOTCHFILTERSCONCLUSIONINTHISPAPERTWOWELLSTRUCTUREDANDCLEARLYARRANGEDMODELSFORBALLSCREWFEEDDRIVESHAVEBEENPRESENTEDADISCRETEANDAHYBRIDDISCRETECONTINUUMMODELBYSEPARATINGTHEPHYSICALCHARACTERISTICSOFTHESHAFTINTOANAXIALANDAROTATIONALSYSTEM,THEBALLSCREWDRIVECOULDBEMODELLEDEXCLUSIVELYUSINGDISCRETEBLOCKSINMATLAB/SIMULINKTHROUGHCOMPARISONWITHTHEMORECOMPLEXHYBRIDMODELITCOULDBESHOWNTHATTHESIMPLIFIEDDISCRETEMODELISWELLSUITABLEFORPREDICTINGTHEMOSTRELEVANTEIGENFREQUENCIESOFAFEEDDRIVEOVERAGREATRANGEOFPARAMETERSSIMULATIONRESULTSSHOWTHATTHEBALLSCREWSHAFTHASADECISIVEIMPACTONTHEOVERALLDYNAMICSOFSUCHADRIVESYSTEMFURTHERMORETHESECONDRELEVANTEIGENFREQUENCYPROVESTOBELESSSENSITIVEWITHRESPEC
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