柔性转子滚动轴承系统混沌行为研究

研究了滚动轴承支承的柔性转子系统的混沌行为。考虑空间Euler-Bernoulli杆单元、刚性圆盘、圆柱滚子轴承非线性接触力、不平衡力，使用有限单元法建立了柔性转子轴承系统的非线性动力学方程组。根据FPA修正法确定求解周期，采用Runge-Kutta法、Newton-Raphson法求解非线性动力学方程组，用获得的系统最大Lyapunov指数判断系统的混沌行为。以某滚子轴承柔性转子系统为例，研究了该类转子系统在径向间隙、不平衡力、转轴刚度比对柔性转子系统混沌特性的影响规律，发现随着轴承径向间隙的增大，系统的混沌区间逐渐增大、变多。不平衡力的存在使得系统混沌的转速及范围变大。随着刚度比增大，振幅峰值及对应的转速均逐渐增大，系统混沌区间也增多，轴承非线性振动对柔性转子系统非线性行为的影响逐渐增强。

Study on Chaos Behavior of Flexible Rotor Rolling Bearing System

A flexible rotor system supported by rolling bearings was studied for chaos, where Euler-Bernoulli shaft element, rigid disk, non-linear contact forces of roller bearings and unbalance force were considered, dynamic equations were established using finite element analysis(FEA) method. Period of solutions were determined by fixed point algorithm(FPA) method, Runge-Kutta method and Newton-Raphson method were used for solving the nonlinear dynamic equations, the largest Lyapunov exponent of the system was obtained to determine the characteristics of the chaotic motion of the system. Taking a flexible rotor roller bearing system for an example, influences of radial clearance, unbalance, stiffness ratio between shaft and bearing on chaos characteristics of the rotor bearing system were analyzed. The results show that chaos range increases with the increase of the bearing radial clearance, unbalanced force has great influence on chaos characteristics of the system, the amplitude of the peak of the curve and the corresponding speed gradually increases and nonlinear behaviors become obviously with the stiffness ratio increases.