摘要
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,利用变步长Runge-Kutta法对系统运动微分方程进行数值求解,构建了系统的Poincaré截面.结合系统的分岔图、相图及Poincaré映射图,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分岔和倍化分岔,给出了系统的分岔值,得到了系统的混沌运动形成过程.
A nonlinear dynamic model for a single-stage spur gear pair system with three degree-of-freedom is established wherein the backlash,the time-varying stiffness,the torsion motion and the transmission error are considered.The nonlinear three-degree-of-freedom equations are solved by employing variable step size Runge-Kutta integration method.The nonlinear dynamic characteristic of the system is discussed for the varying of the exciting frequency and classified based on bifurcation diagrams,phase portraits and Poincaré maps.The Hopf bifurcation and doubling bifurcation are found in the different value of the exciting frequency and their bifurcation points are given.The chaotic motion is obtained.
出处
《兰州交通大学学报》
CAS
2012年第1期65-68,共4页
Journal of Lanzhou Jiaotong University
基金
国家自然科学基金(11172119
10972095)
甘肃省自然科学基金(0803RJZA012
3ZS062-B25-007)
关键词
非线性动力学
混沌
分岔
齿轮
nonlinear dynamics
chaos
bifurcation
gear
