内外激励作用下多自由度齿轮系统的非线性动力学特性

发布时间：2018-05-08 00:34

本文选题：齿轮副 + 非线性动力学　；参考：《振动与冲击》2016年13期

【摘要】：采用周期扩大法,建立了齿轮副的六自由度非线性动力学模型,模型考虑了齿轮副间的时变啮合刚度、齿侧间隙、齿面摩擦等非线性因素;对模型中的相关周期项作傅里叶级数展开,并采用数值积分方法研究六自由度齿轮传动系统的运动随转速、支撑刚度的分岔特性。结合poincaré截面图、分岔图、FFT频谱及最大Lyapunov指数图,系统地分析了支撑刚度对齿轮系统的影响。结果发现,随着激励频率的提高,系统经过多次跳跃进入混沌,提高支撑刚度会使系统的跳跃点数目增加,并且使系统的混沌区减小且整体后移,致使系统推迟进入混沌;再者会使系统通向混沌的道路多样化,除了拟周期通道之外,还出现了激变性、阵发性的混沌道路及"周期5-拟周期-锁相-不稳定吸引子-混沌"的非常规混沌道路。另外支撑刚度的提高会使系统的1/2次谐振加强,致使谐振频率下的动态啮合力(DMF)增大,但会使一些混沌区的DMF逐渐减小,并且使啮合轮齿经历"双边冲击-单边冲击-无冲击"的状态变化。
[Abstract]:The nonlinear dynamic model of gear pair with six degrees of freedom is established by using the method of period expansion. The nonlinear factors such as the time-varying meshing stiffness, tooth side clearance and tooth surface friction are taken into account in the model. The Fourier series expansion of the related periodic terms in the model is carried out, and the bifurcation characteristics of the 6-DOF gear transmission system with rotational speed and support stiffness are studied by numerical integration method. The influence of support stiffness on gear system is analyzed systematically by combining poincar 茅 section, bifurcation diagram and maximum Lyapunov exponent diagram. The results show that with the increase of excitation frequency, the system jumps into chaos many times, and the number of jump points increases with the increase of support stiffness, and the chaotic region of the system decreases and the whole system moves backward, which causes the system to delay entering chaos. In addition to the quasi-periodic channel, there are also some excitatory, paroxysmal chaotic paths and the unconventional chaotic paths of "period 5-quasi-period-phase-locked-unstable attractor-chaos". In addition, the increase of support stiffness will strengthen the 1 / 2 resonance of the system, increase the dynamic meshing force (DMF) at resonant frequency, but decrease the DMF in some chaotic regions. And the meshing gear teeth undergo the state change of "bilateral shock-unilateral impact-no impact".
【作者单位】：华北电力大学机械工程系;
【基金】：国家自然科学基金(51475164) 河北省自然科学基金(E2013502226)
【分类号】：TH132.41

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