单级直齿轮副的共存吸引子特性研究  

Coexisting attractors characteristics of single-stage spur gear pair

作　　者：金花[1] 张子豪 吕小红[1] JIN Hua;ZHANG Zihao;L Xiaohong(School of Mechatronic Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070

出　　处：《振动与冲击》2023年第23期1-7,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(12062008);甘肃省科技计划项目(20YF8WA043;21JR7RA314)。

摘　　要：考虑单级直齿轮副,构建Poincaré映射。应用初值胞映射法、延拓打靶法以及数值仿真求解并追踪系统的共存吸引子及其演化,计算Jacobi矩阵的特征值,根据Floquet理论确定周期吸引子的稳定性与分岔类型,应用胞映射法计算吸引域,研究共存吸引子的分岔特征,揭示系统在极小参数区间存在的容易隐藏的吸引子信息以及鞍结型擦边分岔和混沌激变等不连续分岔行为。在一定参数条件下,单级直齿轮副存在大量的多吸引子共存现象以及周期倍化和鞍结分岔;由于非光滑因素的影响,擦边诱导的鞍结分岔引起系统终态的跳跃和迟滞。研究结果可为直齿轮副动力学行为的评价以及系统参数设计与优化提供指导。Here,a single-stage spur gear pair system was considered,Poincarémapping was constructed.The initial cell mapping method,continuation shooting method and numerical simulation were used to solve and track the system’s coexisting attractors and their evolution,eigenvalues of Jacobi matrix were calculated,the stability and bifurcation type of periodic attractors were determined according to Floquet theory.Attraction domain was calculated using the cell mapping method,and bifurcation characteristics of coexisting attractors were studied.It was shown that easily hidden attractor information and discontinuous bifurcation behaviors,such as,saddle-node type grazing bifurcation and chaotic cataclysm exist in minimum intervals of system parameters;under the condition of certain parameters,there are many coexisting phenomena of multi-attractor,period-doubling and saddle node bifurcation in a single-stage spur gear pair;due to effects of non-smooth factors,grazing-induced saddle node bifurcation leads to jumping and hysteresis of the system’s final state;the study results can provide a guidance for evaluating dynamic behavior of spur gear pair and designing and optimizing system parameters.

关 键 词：齿轮 共存吸引子 稳定性 分岔 激变 

分 类 号：O322[理学—一般力学与力学基础] TH113.1[理学—力学]