滚动轴承-转子系统的分岔分析与多吸引子共存  

BIFURCATION ANALYSIS AND COEXISTENCE OF MULTIPLE ATTRACTORS OF A ROLLING BEARING-ROTOR SYSTEM

作　　者：安慧宁 金花[1] 吕小红[1] 王昕[1] AN HuiNing;JIN Hua;LU XiaoHong;WANG Xin(School of Mechanical 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：《机械强度》2022年第3期554-561,共8页Journal of Mechanical Strength

基　　金：国家自然科学基金项目(12062008);甘肃省自然科学基金项目(20YF8WA043,20JR5RA410)资助。

摘　　要：以滚动轴承支撑下的不平衡转子系统为研究对象,运用变步长Runge-Kutta法进行数值积分获取转子系统的动力学响应。根据增速和减速不同工况下的分岔图、相图和Poincaré映射图分析系统共存吸引子的分岔,揭示其吸引域随系统参数变化的演变过程。结果表明:随着转速的变化,系统在发生Hopf分岔、跳跃分岔和倍化分岔时,会出现吸引子共存的现象。跳跃分岔会导致其吸引域的拓扑结构发生突变,而Hopf分岔和倍周期分岔对其吸引域的影响较小。该研究结果可为系统在不同转速下运行时提供指导,为滚动轴承-转子系统的平稳运行提供理论依据。Taking the unbalanced rotor system supported by rolling bearings as the research object,the variable step size Runge-Kutta method is used for numerical integration to obtain the dynamic response of the rotor system.According to the bifurcation diagrams,phase portraits and Poincarémaps under different conditions of increasing and decelerating,the bifurcation of coexisting attractor is analyzed,and the evolution process of its attraction region with the system parameters was revealed.The results show that when Hopf bifurcation,jump bifurcation and doubling bifurcation occur in the system with the change of rotating speed,there will be the coexistence of attractors.The jump bifurcation will lead to a sudden change in the topological structure of the basin of attraction,while the Hopf bifurcation and the doubling bifurcation have little effect on the basin of attraction.The research results can provide guidance for the operation of the system at different speeds,and provide theoretical basis for the smooth operation of the rolling bearing rotor system.

关 键 词：滚动轴承 转子系统 跳跃分岔 共存吸引子 吸引域 

分 类 号：TH113[机械工程—机械设计及理论]