封闭差动行星齿轮传动系统啮合刚度振动不稳定性.pdf

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1、第52卷第19期机械工程学报Vol.52No.192016年10月JOURNALOFMECHANICALENGINEERINGOct.2016DOI：10.3901/JME.2016.19.025封闭差动行星齿轮传动系统啮合刚度振动*不稳定性12朱增宝朱如鹏(1.安徽理工大学机械工程学院淮南232001；2.南京航空航天大学机电学院南京210016)摘要：不考虑阻尼和外力，建立封闭差动行星传动系统纯扭转自由振动方程并将该方程转换为正则模态方程；利用多尺度法推导出传动系统的啮合刚度波动引起的和型共振频率的稳定性条件并进行动力稳

2、定性分析。研究结果表明：传动系统正则模态方程的啮合刚度波动的一次谐波项的系数矩阵元素绝对值越大，对应该系数矩阵元素的组合共振频率或2倍频引起的振动频率不稳定区间越大；啮合频率接近共振组合频率和2倍频时，不稳定性随啮合刚度波动率的增加而增大；传动系统受封闭级啮合频率激励引起的组合共振频率和2倍频率共振点远比差动级中啮合频率激励引起的多；不稳定三维图中起伏曲面在内外啮合重和度为整数时的点为起伏曲面的谷底，谷底的稳定性高。关键词：封闭差动行星传动；啮合刚度；多尺度法；不稳定性中图分类号：TH132MeshingStiffnessV

3、ariationInstabilitiesinEncasedDifferentialPlanetaryGearTrain12ZHUZengbaoZHURupeng(1.CollegeofMechanicalEngineering,AnhuiUniversityofScienceandTechnology,Huainan232001;2.CollegeofMechanicalandElectricalEngineering,NanjingUniversityofAeronauticsandAstronautics,Nanjin

4、g210016)Abstract：Noconsideringthedampingandexternalforcesthepuretorsionalfreedomvibrationequationofencaseddifferentialplanetarytrainisestablishedandthisequationisconvertedtoregularmodalequation.Themulti-scalemethodisappliedtoderivethestabilityconditionsofsummationr

5、esonancefrequenciescausedbythemeshingstiffnessfluctuationsforthistrainandthedynamicstabilityisanalyzed.Theresearchresultsshowthatthebiggertheabsolutevalueofthecoefficientmatrixelementofthefirstharmonicofthemeshingstiffnessfluctuationsforthisregularmodalequation,the

6、greaterthevibrationfrequencyinstabilityintervalcausedbythecorrespondingcombinationresonancefrequencyorsecondharmonicofthiscoefficientmatrixelement.Theinstabilityisbiggerwiththeincreaseofthemeshingstiffnessvolatilitywhilethemeshingfrequencyisclosetotheresonancecombi

7、nationfrequencyandtwiceharmonicfrequency.Theresonancepointsofthecombinationresonancefrequencyandsecondharmonicfrequencyofthistraincausedbythemeshfrequencyoftheencasedstageisfarmorethanthatofthedifferentialstage.Thepointintheundulatingsurfaceoftheunstablethree-dimen

8、sionalmaptotheintegerofinternalandexternalmeshoverlapisthebottomandithasahighstability.Keywords：encaseddifferentialplanetarytrain；meshingstiffnes