利用有限元法分析陀螺效应对转子振动的影响

Influence of Gyroscopic Effect on Rotor Vibration by Finite Element Method

陀螺效应对转子的临界转速和稳定性均产生影响,尤其在高转速的情况下陀螺效应是不能够忽略的。研究陀螺效应对转子振动的影响,主要包括陀螺效应对转子系统临界转速和稳定性的影响。基于欧拉-拉格朗日方程推导了考虑陀螺效应的回转矩阵,利用有限元法建立考虑陀螺效应的转子数学模型,对数学模型所包含的振动方程进行求解,获得陀螺效应对转子振动影响的相关数据。陀螺效应影响转子的正反涡动的临界转速和稳定性,造成二者的不相等,并且对高阶临界转速和稳定性的影响更明显。

The gyroscopic effect has an influence on the critical speed and stability of the rotor,especially in the case of high speed.In this paper,the effect of gyroscopic effect on rotor vibration is studied,including the effect of gyroscopic effect on the critical speed and stability of rotor system.The rotation matrix is deduced by The Euler Lagrange equation considering gyroscopic effect.Mathematical model is established by using the finite element method.Through solving the vibration equation we obtained the data of gyroscopic effect on rotor vibration.The gyroscopic effect affects the critical speed and the stability of the rotor’s positive and negative vortex,which causes the inequality of the two,and the influence on the high order critical speed and stability is more obvious.