含裂纹复合两级行星轮系振动特性研究  

Vibration property analysis of compound two-stage planetary gear set with crack defect

作　　者：李国彦 李方义[2] 刘浩华[2] 董德浩[3] 张珊珊 LI Guo-yan;LI Fang-yi;LIU Hao-hua;DONG De-hao;ZHANG Shan-shan(Key Laboratory of Advanced Transducers and Intelligent Control System,Ministry of Education,Taiyuan University of Technology,Taiyuan 030024,China;Ministry of Education Key Laboratory of High-efficiency and Clean Mechanical Manufacture,School of Mechanical Engineering,Shandong University,Jinan 250061,China;Shanghai Aerospace Equipments Manufacturer,Shanghai 201100,China)

机构地区：[1]太原理工大学新型传感器与智能控制教育部与山西省重点实验室,山西太原030024 [2]山东大学机械工程学院高效洁净机械制造教育部重点实验室,山东济南250061 [3]上海航天设备制造总厂,上海201100

出　　处：《振动工程学报》2018年第3期500-512,共13页Journal of Vibration Engineering

基　　金：国家高技术研究发展计划(863计划)(2013AA040204);山东省重点研发计划(2017GGX30148)

摘　　要：为揭示复合行星轮系固有特性及裂纹对其振动响应的影响,以工程机械复合两级行星轮系为研究对象,采用集中参数法建立平移-扭转耦合动力学模型,并计入阻尼、支撑、时变啮合刚度、啮合相位等影响因素。根据各构件间相对位移分析,推导系统运动微分方程。将轮齿简化为齿根圆上的悬臂梁结构,根据能量法,分别计算啮合齿轮副赫兹刚度,弯曲刚度,剪切刚度和轴向压缩刚度。推导裂纹轮齿时变啮合刚度计算公式,分析裂纹扩展对时变啮合刚度的影响。进一步对各啮合副的相对啮合相位关系进行推导。采用数值分析方法,求解系统运动微分方程,得到正常及裂纹情况下的系统固有特性,研究时变啮合刚度及裂纹对系统固有频率的影响。综合运用时间历程、阶次谱、相轨迹及Poincaré映射图,分析裂纹扩展对系统非线性振动响应的影响。In this paper,a compound two-stage planetary gear set used in the industrial gearboxes of construction machines is studied in order to illustrate the inherent characteristics and the effects of the crack on the system.A three-dimensional lumpedparameter dynamic model for the gear set is established.Each component has three degrees of freedom：two of translation and one of rotation.The damping,bearing,time varying mesh stiffness and mesh phase relationship are taken into consideration.The relative displacement between two components are derived,and then the equations of motion for the compound planetary gear set are established.In the model,the gear tooth is treated as a cantilever beam on the root circle.Then,the analytical equations are derived to evaluate the time-varying mesh stiffness（TVMS）of a perfect and a cracked gear based on the improved potential energy method,respectively.Furthermore,the effects of the crack propagation on the TVMS are studied.The mesh phase relationships are also derived.Finally,the numerical analysis method is used to solve the equations of motion,and the inherent characteristics of the system with and without the defect are obtained,respectively.The effects of the crack propagation on the natural frequencies of the system are analyzed.Moreover,the influence of crack propagation on the nonlinear dynamic properties of the system are analyzed from the aspects of time history,order spectral analysis,phase trajectory and Poincarémap.

关 键 词：复合行星轮系 时变啮合刚度 裂纹 固有特性 

分 类 号：TH113.1[机械工程—机械设计及理论] TH132.41