摘要
以单自由度直齿圆柱齿轮系统为研究对象,数值计算系统在参数平面上的最大幅值波动云图、幅值叠加图和时间位移映像图,分析系统参数的耦合关系及其对系统动态特性的影响;借助系统的单初值分岔图和最大Lyapunov指数图、多初值分岔图、吸引域图,分析阻尼、时变刚度、综合传递误差、扭矩、啮合频率和齿侧间隙等参数对系统动力学特性的影响规律。研究结果表明:时变刚度与综合误差具有强非线性耦合关系;误差波动和刚度波动耦合作用明显,对齿轮扭转振幅影响较大;合理的齿侧间隙能够抑制或减小系统的振动;系统的每个参数都会引起系统发生分岔,出现吸引子共存,部分参数条件下吸引域存在分形特征。研究结果对齿轮系统的参数选择有一定的理论指导意义。
The dynamic characteristics of a single degree of-freedom spur gear system are studied. The relationship and the matching law between the system dynamical parameters and the influence law of the system parameters are analyzed by the maximum amplitude nephogram of torsional displacement in parameters plane, the register images of amplitude-frequency and the time images of torsional displacement obtained by numerical method. The effects of the system parameters such as damping, the time-varying stiffness, the comprehension transmission error, the torque meshing frequency, the backlash and etc. on the dynamic characteristics are studied according to the diagrams of the single initial value bifurcation and the corresponding Top Lyapunov Exponents, diagrams of multi initial value bifurcation and domains of attraction. The calculation and analysis above may be helpful for selecting the system parameters, which can be applied to design gear systems.
出处
《振动工程学报》
EI
CSCD
北大核心
2017年第2期202-213,共12页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(51365025)
天津市自然科学基金重点资助项目(16JCZDJC38500)
关键词
非线性振动
分岔
齿轮
参数耦合
吸引域
nonlinear vibration
bifurcation
gear
parameters coupling
domain of attraction
