内外激励作用下含侧隙的齿轮传动系统的分岔和混沌  

Bifurcation and Chaos of Gear Transmission System with Clearance Subjected to Internal and External Excitation

作　　者：崔亚辉[1] 刘占生[1] 叶建槐[1] 陈锋[1] 钱大帅[1] 王永亮[1] 

机构地区：[1]哈尔滨工业大学能源科学与工程学院,哈尔滨150001

出　　处：《机械工程学报》2010年第11期129-136,共8页Journal of Mechanical Engineering

摘　　要：为研究支承刚度和齿侧间隙对齿轮-转子系统的分岔和混沌运动的影响,考虑齿侧间隙和内外激励的作用,建立齿轮-转子系统的非线性动力学模型。在对动力学方程进行数值仿真的过程中,为判断齿轮-转子系统的振动是否为混沌运动,采用混沌时间序列分析的方法计算齿轮-转子系统的高维非线性方程的最大Lyapunov指数。结果表明,随着支承刚度的增加,系统的弯扭耦合临界转速也会相应地增大,出现分岔和混沌的区域也随之改变。齿侧间隙对齿轮-转子系统的一阶弯曲临界转速附近的振动的影响较大,当齿侧间隙相对较小时,一阶弯曲临界转速附近的振动相对较好;当齿侧间隙增大到一定值时,一阶临界转速处的振动接近倍周期运动;当齿侧间隙继续增大时,一阶临界转速附近的振动从倍周期运动进入混沌;当齿侧间隙增大到较大值时,一阶临界转速附近的振动迅速转变为混沌运动。混沌时间序列分析方法能有效的计算高维非线性方程的最大Lyapunov指数。In order to investigate the effect of bearing stiffness and gear side clearance on the bifurcation and chaos of gear-rotor system,and with the consideration of the actions of the clearance,internal and external excitation,a non-linear dynamic model of gear-rotor system is built. In the process of numerical simulation of dynamics equation,in order to judge whether the vibration of gear rotor system is chaos or not,the chaotic time series method is used to calculate the maximum Lyapunov exponent of high dimension nonlinear equation of gear rotor system. The results show that with the increase of bearing stiffness,the lateral-torsional critical speed of system increases,the region where bifurcation and chaos appear also changes. The vibration of first order bending critical speed of gear rotor system is affected by clearance greatly. When clearance is relatively small,the vibration of the first order bending critical speed is relatively preferable. When clearance increases to a certain value,the vibration of the first order bending critical speed is double period motion. When clearance continue to increase,the vibration of the first order bending critical speed changes to chaos from double period motion. When clearance increases to a large value,the vibration of the first order bending critical speed turns into chaos rapidly. The maximum Lyapunov exponent of high dimension nonlinear equation can be calculated by chaotic time series analysis method effectively.

关 键 词：混沌 分岔 齿侧间隙 齿轮-转子系统 

分 类 号：TH132[机械工程—机械制造及自动化]