外文翻译-参数化建模滚珠丝杠主轴

毕业设计中英文翻译学生姓名学号学院专业机械设计制造及其自动化指导教师高洪宇0702014425机械工程与自动化学院PARAMETRICMODELINGOFBALLSCREWSPINDLESADADALAUMMOTTAHEDIKGROHAVERLABSTRACTINTHEPRODUCTDEVELOPMENTPROCESSNUMERICALOPTIMIZATIONCANSUCCESSFULLYBEAPPLIEDINTHEEARLYPRODUCTDESIGNSTAGESINTHEVERYCOMMONCASEOFBALLSCREWDRIVES,THEDYNAMICALBEHAVIORISMOSTDEPENDINGONTHEGEOMETRICALSHAPEOFTHEBALLSCREWITSELFPROPERTIESLIKEAXIALANDTORSIONALSTIFFNESS,MOMENTOFINERTIA,MAXIMUMVELOCITYANDACCELERATIONAREDETERMINEDNOTONLYBYTHESERVOMOTORBUTALSOBYSCREWDIAMETER,SLOPEANDBALLGROOVERADIUSFURTHERMORECOUPLINGEFFECTSBETWEENTHEDESIGNVARIABLESMAKETHEOPTIMIZATIONTASKEVENMOREDIFFICULTINORDERTOCAPTURETHESEEFFECTS,EFFICIENTNUMERICALUSUALLYFEMORMBSMODELSARENEEDEDINTHISWORK，ANEWMOREACCURATEANDEFFICIENTMETHODOFCOMPUTINGTHEAXIALANDTORSIONALSTIFFNESSOFBALLSCREWSPINDLESISPRESENTEDWEANALYTICALLYDERIVEPARAMETRICEQUATIONSWHICHDEPICTSMOSTOFTHEDEPENDENCIESOFSTIFFNESSONGEOMETRICALPARAMETERSOFTHESCREWFURTHERMORE,WEENHANCETHEANALYTICALMODELWITHANIDENTIFIEDFUNCTION,WHICHINCREASETHEACCURACYEVENMORETHEPRESENTEDANALYTICALMODELISVALIDATEDAGAINSTFEMMODELANDCATALOGDATAWITHTHEHELPOFNUMEROUSEXAMPLES1INTRODUCTIONTHEAXIALANDTORSIONALSTIFFNESSOFBALLSCREWSPINDLESPLAYSANIMPORTANTROLEINTHEDYNAMICBEHAVIOROFBALLSCREWDRIVES,SINCEITESSENTIALLYDETERMINETHEFIRSTANDSECONDEIGENVALUESOFBALLSCREWDRIVESWHENMODELINGBALLSCREWDRIVESWITHFEMTHETHREADISUSUALLYIGNOREDANDSOMEMEANDIAMETERISUSEDTOMODELASIMPLIFIEDBALLSCREWTHEREFOREITISCRUCIALTOHAVEKNOWLEDGEABOUTTHEBESTAPPROXIMATINGMEANDIAMETERMOSTOFTHEPREVIOUSWORKONMODELINGANDSIMULATINGSTIFFNESSOFBALLSCREWDRIVESCONCENTRATEONMODELINGTHEASSEMBLYBETWEENBALLSCREWNUTANDBALLSCREWSPINDLE,WHICHIMPLIESHIGHACCURACYMODELINGOFCONTACTINJAROSCHCOMPARESTHEORETICALSTIFFNESSOFDIFFERENTTYPESOFBALLSCREWS,BUTTHESPINDLEISTAKENINTOACCOUNTSIMPLIFIEDASANCYLINDERWITHDIAMETEREQUALTOTHESPINDLEOUTERDIAMETER,THUSIGNORINGTHESTIFFNESSWEAKENINGDUETOSPINDLETHREADWITHKNOWLEDGEABOUTTHEREALAXIALKUZANDTORSIONALKUZSTIFFNESSOFASCREWOFUNITLENGTH,AMEANDIAMETERCANBECOMPUTEDWITHTHEHELPOFEKDUZUZM4,（1）AND4,32GKDZZM（2RESPECTIVELY,EYOUNGSMODULUSANDGSHEARMODULUSTHEMEANDIAMETERISALWAYSLESSTHANTHESPINDLEOUTERDIAMETERFOREACHSTIFFNESSWEGETTWODIFFERENTMEANDIAMETERSITDEPENDSONEACHAPPLICATIONWHICHMEANDIAMETERISTHEBESTTOCHOOSEALINEARCOMBINATIONOFTHETWODIAMETERSCOULDALSOBEDONEINGENERALBALLSCREWMANUFACTURERSPROVIDEDATAFORAXIALSTIFFNESSBUTNOTFORTORSIONALSTIFFNESSFORTHISREASONWEUSETHEFINITEELEMENTMETHODFEMTOCOMPUTEBOTHAXIALANDTORSIONALSTIFFNESSOFBALLSCREWSPINDLESBYUSINGAFULLYPARAMETERIZEDFEMODELWECANALSOCOMPUTESTIFFNESSFORNOTEXISTINGBALLSCREWSPINDLESFURTHERMORESINCETHEPARAMETERRANGEISNOTDISCRETIZED,WECANUSETHEMODELINCONJUNCTIONWITHPARAMETEROPTIMIZATIONOFBALLSCREWDRIVESTHEDIFFICULTYHEREISHOWTOEFFICIENTLYCOMPUTETHEAXIALANDTORSIONALSTIFFNESSSOMEWORKSPROVIDEMETHODSFORCOMPUTINGPROPERTIESOFTWISTEDBEAMSBUTONLYFORTHEBENDINGSTIFFNESSORTHEBENDINGEIGENFREQUENCIES,WHICHROLEISLESSIMPORTANTINBALLSCREWDRIVES2DETAILEDPARAMETRICFEMODELDEPICTSOURGENERATIONMETHODOF3DBALLSCREWTHEPROCESSISFULLYAUTOMATEDWITHTHEHELPOFMACROSINTHEFINITEELEMENTSOFTWAREANSYSTHEGEOMETRYOFOURBALLSCREWMODELISPARAMETRIC,SOARBITRARILYGEOMETRIESCANBEGENERATEDTHEGEOMETRYISDESCRIBEDBYTHEFOLLOWINGSIXPARAMETERSSPINDLEDIAMETERD1,SPINDLECOREDIAMETERD2,BALLGROOVERADIUSRS,SPINDLEPITCHPH,SPINDLELENGTHLSANDNUMBEROFTHREADSNTSINCEMANUFACTURERSDOESNOTPROVIDEDATAOFTHEBALLGROOVERADIUS,BUTFORTHEBALLDIAMETERDWINSTEAD,WEUSETHERELATIONSHIPFORTHEOSCILLATIONTODETERMINETHEBALLGROOVERADIUS540WSDRCOMPUTINGTHESTIFFNESSWITHSUCHAMODELCANBEVERYEXACTBUTALSOVERYTIMEEXPENSIVEINORDERTOMINIMIZETHENUMBEROFDEGREESOFFREEDOMBYMAXIMIZINGTHEACCURACYWEDIVIDETHEBALLSCREWINACORECYLINDER09D2ANDTHREADEDCYLINDERTHEMATERIALISMODELEDASLINEAR,ELASTICANDISOTROPICWITHANYOUNGSMODULUS2MN109EANDAPOISSONRATIOV03FIG1MODELINGOFBALLSCREWSPINDLESWITHANSYSINORDERTOCOMPUTETHEAXIALANDTORSIONALSTIFFNESSOFTHEBALLSCREW,WENEEDTOAPPLYANAXIALFORCEANDATORSIONALMOMENTTOONEBALLSCREWENDINTWODIFFERENTSTATICALLYLOADSTEPSTHEOTHERENDOFTHEBALLSCREWHASTOBECONSTRAINEDINTHESAMEDIRECTIONSINORDERTOPREVENTRIGIDBODYMOTIONATTHESAMETIMEBOTHENDAREASOFTHEBALLSCREWSHOULDBEABLETOFREELYEXPANDORCONTRACTINRADIALDIRECTIONWEAPPLYTHESECONSTRAINTSANDFORCESWITHTHEHELPOFSURFACEBASEDCONSTRAINTSONTWOSINGLEPILOTNODESTARGE170THECONSTRAINTSANDFORCESOFTHEPILOTNODESAREDISTRIBUTEDTOTHEENDAREASOFTHEBALLSCREWTHROUGHCONTACTNODESCONTA174ONLYINAXIALANDTANGENTIALDIRECTION,SEEFIG23COMPARISONWITHCATALOGDATAINORDERTOVALIDATEOURMODELWEGENERATED40DIFFERENTMODELSOFBOSCHREXROTHSCREWSPINDLESTHESIMULATIONRESULTSOFTHEAXIALSTIFFNESSCANBECOMPAREDWITHCATALOGDATAWHICHISPROVIDEDBYBOSCHREXROTHASAREFERENCEFORTHECOMPARISONWEUSETHEANALYTICALEQUATIONFORAXIALSTIFFNESS,WHICHCANBEFOUNDINDINISO34084,FORUNITYLENGTHSPINDLE4COS20WUZDDEK3WITHD0NOMINALDIAMETERANDACONTACTANGLEBETWEENBALLANDBALLGROOVEBOTHANALYTICALVALUESANDCATALOGVALUESSHOWS,OTHERASEXPECTED,NODEPENDENCEONTHESPINDLEPITCHBUTTHEINFLUENCEOFSPINDLEPITCHISCONFIRMEDBYTHEFESIMULATIONFURTHERMOREIFWECONCENTRATEONTHEPERCENTALDEVIATIONBETWEENCATALOGANDANALYTICALVALUESANDBETWEENFEMANDANA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IONWITHTHEHELPOFTHEPROPOSEDANALYTICALMETHOD,COMPUTINGSTIFFNESSOFBALLSCREWDRIVESBECOMESMOREEFFICIENTTHANOTHERSTANDARDMETHODSLIKEFEMORSIMPLECATALOGDATAPRACTICALLYWEIMPLEMENTEDTHEINTRODUCEDANALYTICALFUNCTIONSASAMATLABFUNCTIONTHEFUNCTIONGETSTHEGEOMETRICALANDMATERIALDATAOFTHESCREWASARGUMENTSANDCOMPUTESINNEGLIGIBLETIMETHEAXIALANDTORSIONALSTIFFNESSOFTHEBALLSCREWWITHMUCHHIGHERACCURACYTHANWITHOTHERKNOWNANALYTICALMETHODSFORTHEFIRSTTIMETOOURKNOWLEDGEWEHAVEPRECISEINFORMATIONABOUTTHETORSIONALSTIFFNESSOFBALLSCREWS,WHICHISGENERALLYIGNOREDBYMANUFACTURERSTHECOMPUTEDSTIFFNESSCANTHENBEUSEDTOGENERATEDSIMPLEBUTEFFICIENTFEMODELSOFBALLSCREWSTYPICALLYBEAMELEMENTSINTHECONTEXTOFAHOLEMACHINETOOLMODEL,THUSINCREASINGTHEOVERALLEFFICIENCYOFTHEFESIMULATIONNEVERTHELESSANALYTICALLYCAPTURINGOFTHEINFLUENCEOFSPINDLEPITCHCOULDSTILLBEIMPROVED,SUCHTHATBROADERPARAMETERRANGECOULDALSOBEPOSSIBLEACKNOWLEDGMENTSTHISRESEARCHWASSUPPORTEDBYTHEINSTITUTEOFCONTROLOFMANUFACTURINGUNITSSTUTTGARTISW,BYTHEEXCELLENCECLUSTERSIMTECHSTUTTGARTANDGSAMESTUTTGARTTHISSUPPORTISHIGHLYAPPRECIATED参数化建模滚珠丝杠主轴DADALAU米MOTTAHEDI格罗光VERL摘要产品开发过程的数值优化可以成功地应用于产品设计的早期阶段。在滚珠丝杠驱动器很常见的情况下，动态现象大多数根据滚珠丝杠本身的几何形状而定。轴向和扭转刚度相同的丝杠，最大速度和加速度不仅取决于伺服电机，也取决于丝杆直径，凹槽斜率和球半径。此外联轴器的设计参数影响使优化变得更加困难。为了捕捉这些影响，有效的数据（通常是有限元或MBS）模型是必要的。在这项工作中，一个新的更准确和有效的计算滚珠丝杠主轴轴向和扭转刚度被提出。我们分析得到描绘的丝杠几何参数对大多数刚度的依赖关系的参数方程。此外，我们增加一个确定函数的分析模型，从而提高了准确性。在许多例子帮助下，所提出的分析模型针对有限元模型和目录数据进行了验证。1绪论滚珠丝杠主轴的轴向和扭转刚度中对滚珠丝杠驱动器动态特性起着重要作用，因为它基本上决定了滚珠丝杠驱动器的第一个和第二个特征值。当用有限元建模时，滚珠丝杠驱动器的螺纹通常被忽略并且一些平均直径被用来建立简化的滚珠丝杆模型。因此，关键是得到最接近的平均直径。在大多数关于前人建模与仿真下，滚珠丝杆传动建模集中在滚珠丝刚螺母和滚珠丝杠主轴部件。JAROSCH比较了不同类型的滚珠丝杠，但考虑到主轴简化为圆柱体，直径等于主轴外径，从而忽视了削减主轴螺纹。随着了解的实际轴向UZK和单位长度的螺杆扭转刚度ZK，平均直径可以被计算为EDZUZM4,（1）和4,32GKDZZM（2）杨氏模量和剪切模量分别为E和G。平均直径总是比主轴外径小。对于每个刚度我们得到两个不同的平均直径。这取决于每个应用的平均直径的最好选择。这两个直径也可以做到线性组合。一般滚珠丝杠制造商提供轴向刚度数据，但没有扭转刚度。基于这个原因我们使用有限元法（FEM）来计算两者滚珠丝杠主轴轴向和扭转刚度。使用完全参数化的有限元计算模型，我们也可以不用滚珠丝杠主轴刚度。此外，由于参数范围是不离散的，我们可以结合使用滚珠丝杠驱动器参数优化模型。这种方法的困难是如何有效地计算轴向和扭转刚度。有些作品提供了计算扭曲梁的性能计算方法，但只适用于抗弯刚度或弯曲特征频率，它的作用对滚珠丝杠驱动器是不太重要的。2详细的参数化有限元模型图1是我们描述的三维滚珠丝杠生成方法。在有限元软件ANSYS宏的帮助下，这个过程是全自动的。我们的滚珠丝杠几何模型是参数化的，因此可以生成任意几何形状。这几何模型描述是以下六个参数主轴直径D1，主轴直径D2，滚珠槽半径RS，主轴间距PH，主轴长度LS和螺纹NT的数量。由于生产商不提供滚珠槽半径的数据，但提供滚珠直径DW，我们使用了振荡确定滚珠槽半径的关系540WSDR这样的计算模型刚度可以非常准确的，但也很昂贵。为了减少自由度数提高精度，我们划分滚珠丝杠在核心筒（09D2）和带螺纹圆柱。建成线性，弹性和杨氏的弹性模量2MN109E与泊松比03的模型。图1滚珠丝杠主轴建模与ANSYS为了计算滚珠丝杠轴向和扭转刚度，我们需要滚珠丝杠的轴向力和扭矩一个滚珠丝杠应用在两个不同的静态载荷步。滚珠丝杠的另一端必须在同一方向的限制，以防止刚体运动。同时滚珠丝杠两端应该能够在径向方向自由地转动。表面上制约两个单一节点（TARGE170元素），我们运用这些制约因素和力。制约和节点力分布在滚珠丝杠的一端，只有轴向和切向方向（CONTA174）通过接触节点，见图2。3目录数据比较为了验证我们的模型，我们产生的40种不同的BOSCHREXROTH滚珠丝杠主轴的模型。轴向刚度仿真结果与由BOSCHREXROTH提供的目录资料相比，提供了数据。作为对比的基准，我们使用的轴向刚度的分析方程，DINISO34084符合，主轴长度为4COS20WUZDDEK（3）公称直径D0、滚珠和滚珠凹槽之间的接触角。分析数值和产品目录显示，没有依赖主轴螺距。但是，主轴螺距确定了有限元模型。此外，如果我们区分产品目录和分析数值之间有限元和分析数值之间的偏差，我们可以看到产品目录的数据显示的最小的偏差。这可以解释产品目录值仅仅是圆形的分析值。图2应用约束和滚珠丝杠轴轴向力4滚珠丝杠分析模型我们计划推出一滚珠丝杠传动的分析模型，捕捉螺纹的作用。拥有一个精确的分析方法来计算滚珠丝杠刚度的分析方程，并且优先考虑有效率的参数模型，而不是有限元模型，因为那需要大量的迭代。41主要思想对于一个无扭曲统一长度的等截面A和惯性力矩I的主轴，轴向和扭转刚度的分析方程为EAKUZ（4）和GIZ（5）横截面面积为A，极惯性矩为I。滚珠丝杠有固定截面，这截面沿着滚珠丝杠螺纹角为，根据纵坐标Z和主轴间距PH0确定02HPZ（6）螺纹数量的影响丝杠的刚度。在我们的分析方法中，我们假设丝杠轴径A和扭转刚度I正比和，并且和PH0相乘0HUZEAFK（7）和0HZPGIF（8）从公式7和8我们可以看出，我们分析推导滚珠丝杠主轴的刚度的两个步骤分析推导A和I数值计算确定F（PH0）42分析推导截面特性滚珠丝杠螺纹横截面面积的范围为20,1DRC（9）另一条曲线（钟形曲线图3）的形状取决于参数D2，RS和PH0。在我们的推导中，我们认为在大多数情况下，螺纹的轮廓用哥特式形状。这种简化只导致滚珠丝杠刚度的小偏差。为了得到一个钟形解析函数，在图3中我们削减扭曲的圆柱体。图3确定滚珠丝杠横截面积曲线平面垂直于丝杠的纵向轴。忽略了扭曲的圆柱体曲率我们就可以简化，并且生成的段可近似于椭圆形1COS220PHSRPYRDX（10）螺纹斜率APSHPRDP20（11）切割曲线的结果由切割直线Y00切割椭圆得到202COS1PHSKRPRR（12）表示为SRDK21SRK2（13）SPHCO03我们