间隙对含摩擦和时变刚度的齿轮系统动力学响应的影响  

Effect of Backlash on Dynamics of Spur Gear Pair System with Friction and Time-varying Stiffness

作　　者：陈思雨[1] 唐进元[1] 

机构地区：[1]中南大学机电工程学院,长沙410083

出　　处：《机械工程学报》2009年第8期119-124,共6页Journal of Mechanical Engineering

基　　金：国家重点基础研究发展计划(973计划;2005CB724100);国家自然科学基金(50875263)资助项目

摘　　要：主要研究在考虑摩擦和时变刚度时,轮齿间隙对齿轮系统动力学响应的影响。建立常间隙、时变间隙和随机间隙三种不同的间隙形式。利用数值仿真的方法得到系统的幅频响应曲线和时间历程曲线。分析发现:①在低速时,随着摩擦因数的增大,系统响应的方均值和平均分量增大;并经过三次跳跃之后系统进入混沌运动状态;②时变间隙幅值增大导致系统提前进入混沌状态,而且随着时变幅值的增大跳转频率逐渐减小;时变间隙频率较小时,间隙对系统的影响较小;当时变间隙的频率较大时,系统在ω=0.2,0.3时出现明显的共振响应,系统的响应以高频率分量4ω、5ω和6ω为主;③考虑随机间隙时,随着σ的增大,齿轮系统响应的平均分量波动比较大。The chief objective is to study the effect of backlash on nonlinear dynamic response of spur gear pair system with consideration of friction and time-varying stiffness. Three different kinds of backlash, i.e. constant backlash, time-varying backlash and stochastic backlash, are established. The dynamic responses are studied over a wide frequency range by using numerical integration, Runge-Kutta method, to check the nonlinear behavior and jump phenomena in the frequency response. The results indicate that： ① At low speed, with the increase of friction coefficient, the root-mean-square value Xrms and mean value Xm of system response increase, and the system enters into chaotic motion state after three times of jump. ② The increase of amplitude of time-varying backlash causes the system to early enter into chaotic state, and with the increase of time-varying amplitude, the jump frequency decreases gradually. When the frequency of time-varying backlash is small, the influence of backlash on the system is small. When the frequency of time-varying backlash is great, the system produces obvious resonance response at ω=0.2 and ω=0.3.The frequency responses are mainly 4ω, 5ω and 6ω. ③ With consideration of stochastic backlash, the value of Xrms has less change, but Xm has obvious fluctuation.

关 键 词：齿轮 摩擦 时变刚度 间隙 动力学响应 

分 类 号：TH132.41[机械工程—机械制造及自动化]