基于G-P算法关联维数齿轮系统相空间吸引子数值特性  

Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation Dimension

作　　者：林何 Matthias R?tsch 王三民 胥光申 Lin He;Wang Sanmin;Xu Guangshen(School of Mechanical and Electrical Engineering,Xi'an Polytechnic University,Xi′an 710048,China;School of Mechanical Engineering,Reutlingen University,Reutlingen 72762,Germany;School of Mechanical Engineering,Northwestern Polytechnical University,Xi′an 710072,China)

机构地区：[1]西安工程大学机电工程学院 [2]洛特林根大学机械工程学院 [3]西北工业大学机电学院

出　　处：《机械传动》2019年第7期12-16,共5页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51805402);陕西省教育厅科研计划项目(18JK0351);西安工程大学博士科研启动基金(BS1722)

摘　　要：为有效刻画齿轮系统相空间吸引子结构的数值特性,建立了直齿轮系统含间隙与综合传动误差的非线性动力学模型,基于G-P算法推导了等间隔的齿轮系统吸引子关联维数计算公式。对周期运动和混沌运动吸引子,采用Lyapunov指数与关联维数等手段定量表征其数值特性,利用Poin caré截面法定性分析了混沌吸引子的演化和迁移进程。通过关联维数对阻尼比和综合传动误差变化下的混沌吸引子演化行为进行了追踪刻画,结果表明,吸引子结构越复杂则关联维数越大,系统振动越敏感,混沌吸引子关联维数值介于整数1和2之间,具有分数维特征。In order to depict the numerical characteristic of the attractor structure in phase space for gear system effectively,a nonlinear dynamical spur gear transmission model including backlash and general transmis sion error is established,the calculation formula of equispaced gear system correlation dimension is deduced based on G-P algorithm.The numerical characteristics are explored quantitatively for both of periodic attractor and chaotic attractor by employing largest Lyapunov exponent as well as correlation dimension,the evolution and migration process of chaotic attractors is analyzed by means of Poincarésection.The evolution of chaotic at tractor under the excitation of damping ratio and general transmission error is described by correlation dimen sion.The results show that the more complex of attractor structure generates the larger correlation dimension val ues,and causing strong vibration to the system,correlation dimension of chaotic attractor is between integer 1 and 2 with fractal characteristic.

关 键 词：关联维数 LYAPUNOV指数 POINCARÉ截面 混沌吸引子 

分 类 号：TH132.41[机械工程—机械制造及自动化]