封闭差动行星齿轮传动系统啮合刚度振动不稳定性  

Meshing Stiffness Variation Instabilities in Encased Differential Planetary Gear Train

作　　者：朱增宝[1] 朱如鹏[2] ZHU Zengbao ZHU Rupeng(College of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001 College of Mechanical and Electrical Engineering, Nanj ing University of Aeronautics and Astronautics, Nanjing 210016)

机构地区：[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

出　　处：《机械工程学报》2016年第19期25-33,共9页Journal of Mechanical Engineering

基　　金：国家自然科学基金(7150080050);安徽省教育厅自然科学研究重点(KJ2013A093);安徽理工大学博士基金(ZY048)资助项目

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。No considering the damping and external forces the pure torsional freedom vibration equation of encased differential planetary train is established and this equation is converted to regular modal equation. The multi-scale method is applied to derive the stability conditions of summation resonance frequencies caused by the meshing stiffness fluctuations for this train and the dynamic stability is analyzed. The research results show that the bigger the absolute value of the coefficient matrix element of the first harmonic of the meshing stiffness fluctuations for this regular modal equation, the greater the vibration frequency instability interval caused by the corresponding combination resonance frequency or second harmonic of this coefficient matrix element. The instability is bigger with the increase of the meshing stiffness volatility while the meshing frequency is close to the resonance combination frequency and twice harmonic frequency. The resonance points of the combination resonance frequency and second harmonic frequency of this train caused by the mesh frequency of the encased stage is far more than that of the differential stage. The point in the undulating surface of the unstable three-dimensional map to the integer of internal and external mesh overlap is the bottom and it has a high stability.

关 键 词：封闭差动行星传动 啮合刚度 多尺度法 不稳定性 

分 类 号：TH132[机械工程—机械制造及自动化]