动态油膜-柔性转子的分岔与混沌

THE BIFURCATION AND CHAOS OF THE FLEXIBLE ROTOR SYSTEM WITH DYNAMIC p-OIL FILM BEARING SUPPORTS

研究非稳态动载短轴承支撑的Jeffcott柔性转于系统的动力特性,将转速比、不平衡量、阻尼比、黏度作为控制参数,利用Floquet乘子预测周期解的局部稳定性,通过Lagrange插值精细积分法给出系统运动的数值结果并预测系统的长期性态,显示系统在4个参数组合的某些范围内还存在多形式次谐波解,以及由倍周期分岔、二次Hopf分岔通往混沌的现象.将动态油膜力模型和稳态油膜力模型的数值结果进行比较,表明动态非线性油膜力模型的合理性.

The dynamics behaviors of the flexible Jeffcott rotor system supported by unsteady short dynamic journal bearing are investigated. Based on nonlinear unsteady-state dynamic π-oil film force model described by three functions the local stability of the periodic solutions with the controlling parameters, rotational speed ratio, imbalance amount, damping ratio and viscidity, is predicted by using Floquet multiplier. It is found that the period doubling bifurcation is caused by a certain imbalance amount and the Hopf bifurcation is created by the lost stability of the oil-film. By means of the precise integration method with Lagrangian interpolation the trajectory of the shaft center, the Poincaré mapping and the bifurcation graphs are given numerically. The results predicted by the Floquet theory are checked and the long term dynamic behavior of the system is predicted. It is shown that the system has rich nonlinear behaviors at some combination of the four parameters, for examples, multi-frequency subharmonic resonance, as well as chaos phenomenon from doubling bifurcation and twice Hopf bifurcation. Using analytical and numerical methods the local stability, the bifurcation and long term behaviors of the imbalance rotor dynamic system are investigated in a wide range of various parametric configurations. It is concluded the results show that the results of both of the two methods are the same for analyzing local stability of the periodic solutions but after the bifurcation of the periodic solutions the dynamic behaviors of the system with the parameters changed only can be analyzed by numerical method. This is the limitations of the Floquet theory. Combining both methods some suggests on the design parameters of oil-film bearing-flexible rotor system can be offered. Comparing the results for the dynamic oil-film force model to for steady the rationality of the dynamic oil-film force model is noted. The computation results show that the more the imbalance amount, damping ratio and the viscidity, the more the no-synchronization motions of the system will be restrained. The rotational speed of the oil-film lost stability is increased.