多楔带传动系统的频率灵敏度分析

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1、机械工程学报CHINESEJOURNALOFMECHANICALENGINEERING多楔带传动系统的频率灵敏度分析淸华大学基础研究基金资助项口(JC2002016)・侯之超王象武劳耀新(清华大学汽车安全与节能国家重点实验室北京100084)摘要：为了对多楔帶传动系统进行振动分析与设计优化，系统地研究了多楔带传动系统的I占I冇频率对关键设计参数的灵敏度。给出了反映带轮、张紧臂等离散部件转动振动与各段皮带这类弹性体横向振动Z间彼此耦介的运动方程。根据方程耦介与否以及求解的需耍将该系统一分为二。对•丁•具有运动耦合的子系统,建立了矩阵形式的自由振动方程，推导了固

2、有频率对设计参数的通用的灵敏度农达式，由此导出了固有频率对口动张紧机构设计参数和皮带传动速度的灵敏度的显式计算式。针对一多楔带传动系统,计算了固有频率对张紧臂长度、扭转弹簧刚度、安装角以及带速的灵敏度，并运用有限差分法予以验证。关键词：多楔带传动系统耦合振动固有频率灵缴度分析中图分类号：TK414.4SensitivityAnalysisontheFrequenciesofMulti-ribbedBeltDriveSystemsHOUZhichaoWANGXiangwuLAOYaoxin(StateKeyLaboratoryofAutomotiveSafet

3、yandEnergy,TsinghuaUniversity,Beijing100084)Abstract：Inordertostudythevibrationandoptimaldesignofmulti-ribbedbeltdrivesystems,asystematicsensitivityanalysisisconductedonnaturalfrequenciesofmulti-ribbedbeltdrivewidelyusedformodernautomotiveaccessories.Linearequationsofmotionareestab

4、lishedforthesystem,whichreflectthecouplingbetweenrotationalvibrationofdiscreteelementssuchasthepulleysandtensionerarms,andtransverseoscillationofbeltspansthatareaxiallymovingcontinua・Basedoncouplingornotamongvariousdegreesoffreedom,thewholesystemisdividedintotwosub・sys(emsforthesak

5、eofeasysolution・Equationsofmotionaboutthesub-systemwithaforementionedcouplingarearrangedinamatrixform.Derivationsarethenpresented,leadingtoanexplicitexpressionaboutsensitivityofthenaturalfrequencieswithrespecttoanydesignparameterofthesystem・Theexpressionswithrespecttokeydesignparam

6、etersforthetensionerandbeltspeedarethenpresented・Abeltdriveistakenasanexample,towhichsensitivityanalysesareperformedonthenaturalfrequencieswithrespecttobeltspeedandotherdesignparameterssuchasthelengthandinitialorientalangleofthetensionerarm,andtherotationalstiffnesscoefficientofcoi

7、lspringatthepivotofthetensioner.Theanalysesarevalidatedbyresultsfromthefinitedifferencemethodandapreviousapproach.Topreviousliterature,themainenhancementisexplicitexpressionofnaturalfrequencieswithrespecttoanydesignparameterintermsofasetofsystemmatricesoftheequationsofmotion.Theenh

8、ancementmakesiteasiertoper