基于Taylor变换法的转子系统分岔与稳定性研究

BIFURCATION AND STABILITY ANALYSIS OF ROTOR SYSTEMS BASING ON TAYLOR TRANSFORM METHOD

对双盘转子系统的非线性动力学模型 ,引入求解非线性微分方程的Taylor变换法 ,分析转子振动系统动力学特性以及激振频率等参数对系统的影响 ,利用非线性动力学分析中的打靶法求该系统的周期解 ,并利用Floquet主导特征乘子判断不同周期轨道的失稳方式。结果表明 ,考虑非线性油膜力影响后 ,转子系统的运动状态随转速增加由周期至二倍周期再至周期再至拟周期 ,或者经周期运动直接至混沌运动 ,不平衡质量影响转子系统的分岔阈值和分岔类型 。

For a nonlinear dynamical model of a two-disc rotor test-bed was established. By the use of Taylor transform method, the original analysis of the rotor vibration system was transformed to a set of algebraic equations in discrete domain. The dynamical characteristics of the rotor system and the effect of parameters such as frequency on the system were analyzed. Using the shooting method of nonlinear dynamic analysis, the periodic solutions of the system were obtained, and different periodic orbits were judged by the leading Floquet multiplier. The result indicated that the rotor system changed from a periodic motion to a double periodic motion, back to a periodic motion and then a quasi periodic motion, or changed from a periodic motion directly to chaos with the increasing of rotation speed when considering the nonlinear film forces. Mass unbalance will have effect on bifurcation threshold and bifurcation type of the rotor system, and the damping coefficients will affect bifurcation threshold and stability of the rotor system a certain extent.