摘要
为研究齿轮传动系统中齿侧间隙等非线性因素对系统振动特性的影响,综合考虑齿侧间隙、时变啮合刚度、综合啮合误差和轴承纵向响应,建立了三自由度单级直齿轮副传动系统的扭转振动非线性动力学模型;采用变步长4-5阶Runge-kutta法,对系统运动的状态方程进行了数值求解;并构建了系统的Poincaré截面,得到了系统的分岔图。结合系统最大Lyapunov指数谱、Poincaré映射图及FFT频谱图,分析了系统在激励频率变化时的动力学特性,发现系统在不同激励频率下会发生Hopf分岔、鞍结分岔及倍化分岔,给出了系统的分岔值,分别得到了系统经Hopf分岔和鞍结分岔通向混沌运动的两种过程。
Abstract： In order to investigate the influence of the backlash and other nonlinear factors to system vibration, a nonlinear dynamic model of a single-stage spur gear pair system with three degree-of-freedom is established in this paper, wherein the backlash, the time-varying stiffness, the torsion motion and the transmission error are consid- ered. The nonlinear three-degree-of-freedom equations are solved by employing variable step-size Runge-kutta meth- ods and the bifurcation diagrams are obtained. The nonlinear dynamic characteristic of the system is discussed for the varying of the exciting frequency, classified based on bifurcation diagrams, top Lyapunov exponent （TLE） dia- gram, Poincar6 maps and FFT spectrum. The Hopf bifurcation, saddle-node bifurcation and doubling bifurcation are found in the different values of the exciting frequency and their bifurcation points are given. There are two routes from periodic motion to chaos motion. The one is from period-4 motion to chaos by Hopf bifurcation, and the other is from period-3 motion and period-3 by saddle-node bifurcation.
出处
《机械科学与技术》
CSCD
北大核心
2014年第2期199-203,共5页
Mechanical Science and Technology for Aerospace Engineering
基金
国家自然科学基金项目(51365025
11172119)资助
关键词
动力学
非线性系统
Runge—kutta法
齿轮
HOPF分岔
chaos theory
degrees of freedom （mechanics）
differential equations
dynamics
errors
Fast Fourier Transfer
gears
Hopf bifurcation
Lyapunov methods
nonlinear systems
Runge-kutta methods
