考虑切向刚度变化裂纹转子的分叉与混沌  

Study on bifurcation and chaos of cracked rotor considering tangential stiffness variation

作　　者：沈新亮[1] 邹剑[1] 陈进[2] 董广明[2] 

机构地区：[1]青岛农业大学机电工程学院,山东青岛266109 [2]上海交通大学机械系统与振动国家重点实验室,上海200240

出　　处：《机械设计》2014年第11期101-107,共7页Journal of Machine Design

基　　金：国家自然科学基金资助项目(10176014);山东省优秀中青年科学家奖励基金资助项目(BS2009ZZ009);山东省高等学校科技计划资助项目(J09LD08)

摘　　要：基于不附加任何假设的裂纹模型,考虑切向刚度变化,建立裂纹转子无量纲动力学模型,可适用于瞬态、稳态、非线性等不同运动状态。采用分叉图、Pioncaré映射、轴心轨迹、频谱图、最大Lyapunov指数等,分析裂纹法向刚度变化、切向刚度变化、质量偏心与质量偏心角对裂纹转子分叉与混沌特性的影响,发现:随着裂纹法向刚度变化的增加,裂纹转子在亚临界转速区出现倍周期分叉、拟周期、周期3解等振动形式;考虑裂纹切向刚度变化,裂纹转子在1/2,2/3亚临界转速区出现拟周期、混沌运动,进入混沌的途径与拟周期、周期3解有关;质量偏心的增加或质量偏心角180°时,对裂纹转子的非线性运动具有明显的抑制作用。数值仿真研究可为工程实际中裂纹转子故障诊断提供依据。Based on the crack model without any assumption, the dynamic equation of a cracked rotor in dimensionless form was modeled considering the tangential stiffness variation.The model could be applied to transient, stationary and nonlinear states. Bifurcation diagram, Pioncare map, orbit, frequency spectrum and Lyapunov exponent were used to analyze the influence of the stiffness variations in vertical and tangential directions, the unbalance and unbalance angle on bifurcation and chaos of cracked rotor. With the increment of stiffness variation in vertical direction, the nonlinear dynamic behaviour appeared such as period doubling bi- furcation, quasiperiodic motion and period-3 solution near the subcritical speed ratio. Quasiperiodic motion and chaos occurred near the subcritical speed ratios and in view of the tangential stiffness variation.The routes to chaos were related to quasiperiodic motion or period-3 solution. The nonlinear vibration decreased when the unbalance increased or the unbalance angle was. Numerical simulation provides a basis for fault diagnosis of cracked rotor in engineering practice.

关 键 词：裂纹转子 切向刚度变化 质量偏心 分叉 混沌 

分 类 号：TH113.1[机械工程—机械设计及理论]