含轴承间隙不平衡转子系统的动力学特性分析

Analysis on the dynamic characteristics of an unbalanced rotor system with bearing clearance

将考虑轴承间隙的不平衡转子系统作为研究对象,建立系统的无量纲非线性微分方程,采用4阶龙格库塔变步长求解,通过计算机软件模拟得到非线性动态响应,综合运用分岔图、相图、最大碰摩力变化图研究了转速、阻尼系数、摩擦因数等参数改变对系统微分方程解的拓扑结构和稳定性的影响。研究表明:阻尼系数和摩擦因数在适当的参数域系统拓扑结构呈周期性,系统趋于稳定,在较小的阻尼系数和摩擦因数参数域系统处于混沌状态,转子轴承间隙内最大碰摩力变化明显;转速对系统的影响在小参数域处于混沌状态,在其他参数域系统解趋于稳定,拓扑结构呈周期性变化,其最大碰摩力在特定参数域出现峰值,而在实际的转子系统设计中应避开转子系统呈混沌状态或最大碰摩力出现峰值的参数域,从而提高转子系统的使用寿命。

In this article,with the focus on an unbalanced rotor system with bearing clearance,the dimensionless equations of the system are worked out.The nonlinear dynamic response of the equations is identified by means of numerical integration.The effects of changes in parameters such as speed,damping coefficient,and friction coefficient on the topological structure and stability of the differential equations are explored with the aid of bifurcation diagrams,phase diagrams,and maximum frictional force diagrams.The research shows that both the damping coefficient and the friction coefficient are periodic in the appropriate parameter domain,and the system tends to be stable.In the parameter domain of smaller damping coefficient and friction coefficient,the system is chaotic,and the maximum frictional force changes obviously in the rotor’s bearing clearance.The effect of speed on the system is chaotic in the small parameter domain,the system solution stabilizes in other parameter domains,and the topology changes periodically.The maximum friction force peaks in the specific parameter domain.In the actual design,the parameter range where the rotor system is chaotic or the maximum rubbing force reaches the peak should be avoided,so as to improve the service life of the rotor system.