齿轮传动系统随机振动模型与仿真  

Stochastic Vibration Model and Simulation of Gear Transmission System

作　　者：王靖岳[1] 郭立新[1] 张亮[2] 王浩天[3] 

机构地区：[1]东北大学机械工程与自动化学院,辽宁沈阳110819 [2]沈阳理工大学汽车与交通学院,辽宁沈阳110159 [3]沈阳航空航天大学研究生学院,辽宁沈阳110136

出　　处：《东北大学学报（自然科学版）》2013年第4期578-582,共5页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(50875041);新世纪优秀人才支持计划项目(NCET-08-0103);中央高校基本科研业务费专项资金资助项目(N110403008);辽宁省教育厅科技研究项目(L2012068)

摘　　要：除考虑齿轮的齿侧间隙、时变啮合刚度、综合啮合误差和轴承纵向响应外,还考虑了由扭矩波动引起的低频外激励和齿轮阻尼比、齿侧间隙、激励频率、啮合刚度的随机扰动,根据牛顿定律建立了单对三自由度直齿齿轮传动系统的动力学方程.利用系统的分岔图、相图、时间历程图、Poincaré映射图、李雅普诺夫指数和功率谱图分析了齿轮传动系统在齿轮时变啮合刚度变化下的动力学特性,以及啮合刚度的随机扰动对系统动力学的影响.数值仿真表明,随着齿轮时变啮合刚度的增大,齿轮传动系统从周期运动通过倍化分岔通向混沌运动;在啮合刚度的随机扰动不是很大时,系统解的周期结构不会发生大的变化.Considering the gear backlash, time-varying mesh stiffness, gear comprehensive error and bearing longitudinal response, as well as a low-frequency external excitation caused by the torque fluctuation and the random disturbances of damping ratio, gear backlash, excitation frequency and meshing stiffness, a dynamic equation for a single pair of three degrees of freedom spur gear system was established according to Newton＇ s laws. Using the bifurcation diagram, phase diagram, time history chart, Poincar6 map, Lyapunov exponents and power spectrum of the system, the dynamic characteristics of the gear transmission system under the change of time- varying meshing stiffness were analyzed, as well as the effect of the meshing stiffness random disturbance on the system dynamics. Numerical simulation results showed that the gear transmission system will transform from the period motion to chaos motion by doubling bifurcation with increasing the time-varying meshing stiffness. When the meshing stiffness random disturbance is not big, the periodic structure of the system solution won＇ t change much.

关 键 词：齿轮传动系统 随机振动 混沌 POINCARÉ映射 分岔 

分 类 号：TH132.41[机械工程—机械制造及自动化] O324[理学—一般力学与力学基础]