随机外干扰下齿轮传动系统的混沌振动分析  

Chaotic Vibration Analysis of Gear Transmission System with Stochastic Disturbance

作　　者：王靖岳[1,2] 王浩天[3] 郭立新[2] 

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

出　　处：《振动．测试与诊断》2014年第6期1099-1104,1172,共6页Journal of Vibration,Measurement & Diagnosis

基　　金：国家自然科学基金资助项目(51275082);新世纪优秀人才支持计划资助项目(NCET-08-0103);辽宁省教育厅科技研究资助项目(L2012068);沈阳理工大学机械设计及理论重点学科开放基金资助项目(4771004kfx08)

摘　　要：为了考察输入力矩的随机扰动对系统动力学的影响,综合考虑由扭矩波动引起的低频外激励、齿轮阻尼比、齿侧间隙、激励频率和啮合刚度的随机扰动因素,根据牛顿定律建立单对三自由度直齿齿轮传动系统的随机动力学方程。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齿轮传动系统在齿轮激励频率变化下的动力学特性,并分析输入力矩引起的随机外扰动对系统分岔特性的影响。数值仿真表明:随机非光滑齿轮传动系统存在着丰富的倍周期分岔现象;随着齿轮激励频率的增大,齿轮传动系统先通过周期倍化分岔从周期运动到混沌运动,再通过逆周期倍化分岔从混沌运动通向周期运动;随着输入力矩随机扰动的增大,会对系统的随机分岔区域和系统动力学特性产生本质影响。In order to study the effects of stochastic disturbance of the input torque on system dynamics,the dynamics equations of a single pair of three degrees of freedom spur gear system are established according to Newton's law,while considering stochastic disturbance of a low frequency external excitation caused by torque fluctuation damping ratio,gear backlash,excitation frequency and meshing stiffness.Using the bifurcation diagram,phase diagram,time history chart,Poincare map,Lyapunov exponents and power spectrum of the system,the dynamic characteristics of the gear transmission system in gear excitation frequency changing are analyzed,as well as the influence of stochastic disturbance caused by the input torque on the system bifurcation characteristic.Numerical simulation results show that the stochastic non-smooth gear transmission system has a wealth of period-doubling bifurcation.As the gear excitation frequency increases,the gear transmission system turns from periodic motion into chaos via period-doubling bifurcation,then back to periodic motion via inverse period-doubling bifurcation.When the stochastic disturbance caused by the input torque increases,it will affect the stochastic bifurcation area and the dynamic characteristics of the system.

关 键 词：齿轮传动系统 随机扰动 李雅普诺夫指数 周期倍化分岔 随机分岔 

分 类 号：O322[理学—一般力学与力学基础] TH132.41[理学—力学]