转子动力学与DyRoBeS简介

转子动力学与DyRoBeS简介2012.09.10中国Ÿ哈尔滨提纲Ø转子动力学基本知识ØDyRoBeS-Rotor软件Ø例题分析第一部分转子动力学基本知识1.1转子-轴承-基础1.2转子动力学基础1.3转子振动方式1.4转子振动分析1.5转子-轴承-基础系统模型1.1转子-轴承-基础对于任何旋转机械，主要着眼于机器的结构尺寸、功能、转速等，不论是大型旋转机械还是微型旋转机械，其建模和分析方法类似。任何旋转机械包含三部分：转子，轴承及其支撑部件。具体结构物理模型数学模型模型的解1.1转子-轴承-基础●研究对象：旋转机械转子及其相关部件、结构的动力学特性。●研究内容：动态振动、响应、疲劳、强度、可靠性、稳定性、状态监测以及故障诊断和控制。●研究范围：转子系统动力学建模及其分析计算方法；转子系统临界转速的求解；振型与不平衡响应；转子系统稳定性分析；支承转子的各类轴承的动力学特性；转子的平衡技术；转子系统的故障机理及动态特性；故障的监测方法及诊断技术；密封动力学；非线性的振动、分叉与混沌；转子系统的动态响应测试和分析技术；系统电磁激励和机电藕联振动；系统振动和稳定性控制技术。1.2转子动力学基础1.2转子动力学基础正进动：涡动方向Ω与转子旋转方向ω相同的涡动。反进动：涡动方向Ω与转子旋转方向ω相反的涡动。涡动概念：转轴中心围绕轴承中心所做的转动。转子的涡动(横向弯曲振动)假设有一恒定Ω，由牛顿运动定律可求出质心的运动方程：1.2转子动力学基础1.2转子动力学基础Flexible,MasslessShaftUnbalancedDiskFlexibleBearingsm,eKsKbx,KbyCbx,Cby转子-轴承模型GeneralizedLaval-JeffcottrotorRigidBearingsTheLaval-Jeffcottrotor引起机组振动故障的常见原因1.2转子动力学基础支撑动刚度激振力结构刚度共振连接刚度转子不平衡轴系连接同心度和平直度不均衡电磁力轴瓦振动轴振动普通强迫振动自激振动轴瓦自激参数振动汽流激振1.3转子振动方式转子的振动方式：lLateralVibration：横向振动lTorsionalVibration：扭转振动lAxialVibration：轴向振动1.3.1LateralVibration高速旋转机械中，转子横向振动占主导。它会引起轴涡动，产生故障，甚至会引起转子（叶片）与定子（外壳）碰磨，产生严重的机械故障。LateralVibration1.ModelSummary2.StaticDeflection&BearingLoads3.CriticalSpeedAnalysis4.CriticalSpeedMap5.WhirlSpeed&StabilityAnalysis6.SteadyStateSynchronousResponse-LinearSystem7.SteadySynchronousResponse-NonLinearSystem8.TimeTransientAnalysis9.SteadyStateHarmonicExcitationResponse10.SteadyManeuverLoadAnalysis1.3.2TorsionalVibration扭转振动，旋转振动模态阻尼很小，模态阻尼比一般取0.01-0.1。在高速旋转机械中，一般很难检测。TorsionalVibration1.ModelSummary2.NaturalFrequenciesandModes3.SteadyStateForcedResponse4.TransientResponsebyTimeDependentExcitations5.StartupTransientAnalysis(SpeedDependentExcitations)1.3.3AxialVibration轴向振动，引起轴向窜动，尤其在齿轮啮合中。一般机械使用止推轴承来消除轴向窜动。1.ModelSummary2.NaturalFrequenciesandModes3.SteadyStateForcedResponseAxialVibration1.4转子振动分析UnstretchedPositionStaticEquilibriumPositionStaticEquilibriumPositionUndeformedPositionf(t)f(t)mgmgkkccmmzzxx单自由度振动：DiskKsM,eKbx,KbyCbx,Cby()mzczkzmgft++=+&&&,zxkmg=+ΔΔ=Z=undeformedposition(bearinggeometrycenter)x=staticequilibriumposition()())(hpxttxxt=+()mxcxkxft++=&&&振动方程：1.4转子振动分析xxCxxKyyCyyKxyCxyKyxCyxKxxxyyxyyCCCCxxxyyxyyKKKKxxyy⎡⎤⎡⎤⎧⎫⎧⎫+⎨⎬⎨⎬⎢⎥⎢⎥⎩⎭⎩⎭⎣⎦⎣⎦&&轴承简化模型：1.4转子振动分析1.4.1自由振动00(0),(0)xxxx==&&0mxxckx++=&&&2,1ndnkm==-22,21ncmpxxdwx==-iidijslw=±2221dpspxdwx-==-22(2)dxpd=+特征值：阻尼指数阻尼固有频率1.4转子振动分析tx(t)0.2x=1x=1.4x=3.临界阻尼是按指数规律衰减的非周期运动，比过阻尼衰减快三种阻尼情况比较：1x1x=1x欠阻尼过阻尼临界阻尼1.欠阻尼是一种振幅逐渐衰减的振动2.过阻尼是一种按指数规律衰减的非周期蠕动，无振动发生1.4.1自由振动C=0.2C=0.2C=0C=0C=0.6C=0.6C=1.2C=1.21.4.1自由振动C=0C=-0.6C=-0.2C=-1.51.4.1自由振动12231=lnlnlniixxxxxxd+⎛⎞⎛⎞⎛⎞==⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠1.4.1自由振动1x2x3x1.4.2强迫振动)cos()(f-Ω=tXtx210Ω=emF惯性力弹性力阻尼力激励力从右图可知，激振力F0为：振幅X为：滞后相位角为：22220)()(XcXmkXFΩ+Ω-=2220)()(Ω+Ω-=cmkFX)(tan21Ω-Ω=Φ-mkctFkxxcxmexcwcos0=++&&&1.Unbalance2.ShaftBow3.HarmonicExcitation4.StaticLoad1.4.2强迫振动常见强迫振动1.SteadyStateResponse-Unbalance1.4.2强迫振动1.4.2强迫振动2.SteadyStateResponse–shaftbow1.4.2强迫振动3.SteadyStateResponse–harmonicexcitation1.4.2强迫振动4.SteadyStateResponse–staticload1.4.2强迫振动5.SteadyStateResponse–alltogether1.5转子-轴承-基础系统模型RotorSystemConfiguration1.5转子-轴承-基础系统模型Rotor-bearing-supportsystemconfiguration1.5转子-轴承-基础系统模型第二部分Dyrobes-rotor2.1前处理2.2计算分析2.3后处理2.4Tools2.5Dyrobes-rotor常用模块Dyrobes-rotorThelateralvibrationofthediscretizedsystemisdescribedbytwotranslational(x,y)andtworotational(θx,θy)coordinatesateachfiniteelementstation.Themotionofaflexiblesupportisdescribedbytwotranslationaldisplacements(x,y).Theanalysesforlateralvibrationcontain:StaticDeflectionandBearing/ConstraintReactionsCriticalSpeedAnalysisCriticalSpeedMapAnalysisWhirlSpeedandStabilityAnalysisSteadyStateSynchronousResponseAnalysis–LinearSystemSteadyStateSynchronousResponseAnalysis–NonLinearSystemTimeTransientAnalysisSteadyStateHarmonicExcitationResponseAnalysisSteadyManeuverLoadAnalysis2.1前处理-总体概述Fortorsionalvibration,themotionofeachfiniteelementstationisdescribedbyarotationaldisplacement(θz)aboutthespinningaxis.Thesystemscanbecontinuous,discrete,orthecombinationofcontinuousanddiscreteelements.Theanalysesfortorsionalvibrationare:NaturalFrequenciesandModesCalculationSteadyStateForcedResponseAnalysisTransientAnalysis(TimeDependentExcitations)StartupTransientAnalysis(SpeedDependentExcitations)Forforcedresponseanalysesincludingthetransientanalysis,themodaldampingcanbespecifiedifthedirectdampingisnotreadilyavailable.2.1前处理-总体概述Foraxialvibration,themotionofeachfiniteelementstationisdescribedbyatranslationaldisplacement(z)alongthespinningaxis.Similartothetorsionalmodel,thesystemscanbecontinuous,discrete,orthecombinationofcontinuousanddiscreteelements.Theanalysesforaxialvibrationare:NaturalFrequenciesandModesCalculationSteadyStateForcedResponseAnalysisSeveraldesignTools:AerodynamicCrossCouplingCalculation,RollingElementBearingStiffnessCalculation,LiquidAnnularSealDynamicCoefficients,GasLabySealDynamicCoefficients,SqueezeFilmDamperStiffnessandDampingCalculation,Mass/InertiaPropertiesCalculation,RotorOrbitAnalysis,BalancingCalculation,andAuto-BalancingAnalysis.2.1前处理-总体概述DataUtilizationforLateral,Torsional,andAxialAnalysis2.1前处理-总体概述2.1前处理已知：1.结构尺寸：离散化2.材料：密度，弹性模量，剪切