不平衡磁拉力作用下裂纹转子系统的分岔  

Bifurcation of a Cracked Rotor-bearing System under Unbalanced Magnetic Pull

作　　者：黄志伟[1] 周建中[1] 贺徽[1] 张孝远[1] 王常青[1] 

机构地区：[1]华中科技大学水电与数字化工程学院,武汉430074

出　　处：《机械工程学报》2011年第13期59-64,共6页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51079057);'十一五'国家科技支撑计划重大(2008BAB29B05)资助项目

摘　　要：针对大型旋转机械转子系统机电耦合具有强非线性特征的问题,根据磁拉力与转子偏心的关系,推导出不平衡磁拉力(Unbalanced magnetic pull,UMP)的解析式,建立UMP作用下裂纹转子—轴承系统的动力学模型,并采用数值积分方法研究此类裂纹转子的分岔与混沌特性。通过分岔图、Poincaré图和频谱幅值图分析UMP和裂纹深度对转子运动的影响,结果表明:UMP使转子系统随速度变化的典型动力学响应有所提前,振幅增大,幅值谱图中出现了连续幅值较大的谐波分量;随着裂纹深度的不断增加,转子系统在亚临界转速区出现了短暂的混沌运动,在临界转速附近的混沌区域不断减小,其混沌特征有所变化,且进入混沌区域的倍周期分岔运动基本消失,而在超临界转速区则出现了较长的周期7运动。研究结果为深入解析机电耦合转子系统故障机理提供有益的理论参考。Electromagnetic vibration in rotating machinery is endowed with nonlinear characteristic due to the mechanic and electromagnetic coupling.According to the nonlinear relation of unbalance magnetic pull（UMP） with respect to rotor eccentricity,an analytical expression of UMP is deduced and a kinetic equation is set up to express electromagnetic vibration characteristics of a cracked rotor-bearing system with nonlinear oil film.Numerical method is adopted to analyze bifurcation and chaos characteristics of the system.The influence of UMP and crack depth on rotor movement is analyzed through Poincaré maps,amplitude spectrum and bifurcation diagrams.Simulation results reveal that dynamic responses of this system advance to occur due to UMP and the amplitude increases.The spectrum is composed of continuous and broad band frequencies.As crack depth increases,transitory chaotic motion of the rotor system appears in the sub-critical speed region.But the chaotic motion region decreases and its characteristics change around the critical speed,where period-doubling bifurcation almost disappears.And in the supercritical speed domain there is a long region for period-seven.It is indicated that this research may contribute to further understanding of failure mechanism of such a rotor-bearing system with the mechanic and electromagnetic coupling.

关 键 词：不平衡磁拉力 转子轴承系统 裂纹模型 分岔 混沌 

分 类 号：TH113[机械工程—机械设计及理论] O322[理学—一般力学与力学基础]