一种转子系统混沌运动转速范围确定方法

Nonlinearity measure based speed identification for chaotic behaviors of rotor systems

转子系统的混沌运动容易引起其自身产生疲劳损伤并可能造成运行失稳,因此在设计和运行过程中应避开该转速区域。本文提出一种基于动力学行为非线性度量的转子系统混沌运动转速范围确定方法,根据转子系统非线性度量值的增长趋势和波动性质来确定混沌运动的转速范围。文中首先介绍了系统非线性度量的含义,以具有某设定支承松动间隙的转子系统为例,建立转子-轴承系统的动力学模型并在所研究转速范围内进行数值计算研究,发现系统具有周期、拟周期、混沌运动等变化的运动状态。对动力学模型的非线性项进行泰勒展开获得线性近似模型,比较两个模型之间的动力学行为差异,得到转速-非线性度量值曲线图,从而准确地描述转子系统运动状态随转速的变化。利用3σ方法设定初始阶段非线性度量值增长的阈值,可确定转子系统动力学行为出现初始分岔点的转速,再利用非线性度量值的波动性质,可确定转子系统混沌运动转速范围。将该方法获得的结论与计算得到的分岔图进行对比,说明了方法的准确性。方法对于转子-轴承系统在设计和运行过程中避开混沌运动转速范围具有一定的理论指导作用。

The chaotic behaviors can lead to the rotor system to be fatigue and unstable,which should be avoided in the process of design and operation.In this paper,a nonlinearity measure based speed identification method is proposed for rotor-bearing systems.Firstly,the definition of nonlinearity measure is given and the dynamical model for a rotor-system with a given pedestal loose clearance is established.The simulations have found that its dynamic behaviors have cycles,quasi-periods,and chaotic motions within the studied speed range.The difference of the dynamic behavior between the nonlinear model and the linear approximation are compared and quantified,while the relationship between rotor speeds and the values of nonlinearity measure is established.The initial speed for bifurcation can be determined by the alarm threshold calculated by 3σmethod,while the fluctuation range of nonlinearity degrees can be used to find the rotating speed range for chaos behaviors.