斜齿轮柔性转子轴承系统非线性动力学分析

Nonlinear Dynamics Analysis of Flexible Rotor Bearing System with Helical-gear

考虑齿侧间隙、轴承径向间隙、齿轮不平衡力,使用有限元法建立质量矩阵、刚度矩阵、阻尼矩阵并组装成整体参数矩阵,建立了适用于斜齿轮柔性转子滚动轴承系统的非线性动力学模型。采用Runge-Kutta法求解,并分析系统的动力学行为。研究了转速、转轴刚度、不平衡力对斜齿轮系统非线性动力学行为的影响规律。结果表明:随着转速的变化,系统将经历周期、拟周期、混沌等多种运动状态;随着转轴刚度的减小,混沌运动的区间减小,振幅大小发生改变;不平衡力增大后,系统混沌区间增大,混沌运动的区间也发生改变。

Considering backlash, radial clearance of bearing and unbalance force, the mass, stiff- ness and damping matrixes of a rotor system were obtained by using finite element method, then they were assembled by an integrated method. Nonlinear dynamics model of a flexible rotor bearing system with helical-gear was established. Runge-Kutta method was used to solve nonlinear dynamics equa- tions, and the dynamic behaviors of the system were analyzed. The nonlinear dynamics behaviors of the flexible rotor bearing system with helical--gear were discussed for effect of speed, shaft stiffness and unbalance. The results show that periodic, quasi--periodic and chaos motion occur as the speed changes. With the decrease of shaft stiffness, the range of chaos motion is decreased and the ampli rude is also changed. As the unbalance increases, the range of chaos motion state is increased and range of the chaotic motion is changed.