摘要
考虑含齿侧间隙、时变啮合刚度、综合啮合误差等因素下的单自由度直齿轮系统动力学模型。利用Melnikov方法对系统同宿轨线出现分岔及马蹄混沌的参数区域进行了预测。采用变步长Runge-Kutta法对单自由度运动微分方程进行了数值求解。结合系统的相图、庞加莱截面图以及最大李雅普诺夫指数,分析了系统随内部误差激励力变化时的动力学特性,得到系统的混沌运动规律。数值模拟的结果和Melnikov方法预测的系统出现同宿分岔和混沌的参数区域相吻合。
The dynamic model of single-degree-of-freedom spur gear system is considered considering the factors such as tooth side clearance,time varying meshing stiffness and comprehensive engagement error. The parameters of bifurcation and horseshoe chaos are predicted by Melnikov method. The variable step size Runge-Kutta integration method is used to solve the differential equations of singledegree-of-freedom motion. Combined with the phase diagram of the system,the Poincaré section and the largest Lyapunov exponent,the dynamic characteristics of the system with the change of the internal error excitation force are analyzed,and the chaotic motion of the system is obtained. The results of the numerical simulation are consistent with those of the system in which the Melnikov method predicts the homoclinic bifurcation and chaos.
出处
《重庆理工大学学报（自然科学）》
CAS
北大核心
2018年第1期92-99,共8页
Journal of Chongqing University of Technology：Natural Science
基金
国家自然科学基金资助项目(11672249
11732014)
