弹性叶片-轮盘-转轴系统的耦合振动特性

Vibration characteristics of an elastic blade-disk-shaft coupling system

首先考虑各组件陀螺效应推导了旋转状态下转轴-轮盘及叶片的连续体能量方程并进行离散化和组集处理,获得了柔性转子-叶片耦合系统的运动微分方程。然后分析了叶片数和轮盘位置对系统固有频率的影响。通过对比分析发现,由于叶片和转轴的耦合出现了由叶片前两阶模态主导的转子-叶片耦合模态和叶片-叶片耦合模态,其中包含Nb-2(Nb为叶片数目)个重复的叶片-叶片耦合模态,2个重复的转子-叶片耦合模态;随着叶片数的增加,转子模态固有频率线性减小,叶片-叶片耦合模态的固有频率不变,转子-叶片耦合模态的固有频率线性增大;转子-叶片耦合模态和转子前两阶模态对应的固有频率均受轮盘位置影响,影响趋势关于转轴中点对称;其中,转子-叶片耦合模态对应的一阶固有频率在轮盘从轴端到中点过程中逐渐增大,在轴中点时达到最大,二阶固有频率在轮盘从轴端到中点过程中先增大后减小,在轴中点时达到最小;转子模态固有频率变化则与转子-叶片耦合模态完全相反,但不同的是其基本不受叶片数影响。

The continuous physical equations in rotation of the shaft-disk and the blades are deduced, discretized and group-set- ting processed, respectively. Then, the motion differential equation of a flexible rotor-blade coupling system is established. The gyroscopic effect is also taken into consideration in the derivation work to guarantee the accuracy of the calculation at the same time. The influences of the number of blades and the position of the disk on the natural frequencies of the system are ana- lyzed on the basis. It is found that there are two coupling modes~ shaft-blade （SB） and blade-blade （BB） due to the coupling between blade and shaft through comparative analysis. The inter-blade （BB） modes are of repeated frequencies of （Nb- 2） multiplicity for number blades, and the shaft-blade （SB） modes are of repeated frequencies of （2） multiplicity for number blades. With the increase of the number of blades, the natural frequencies of the rotor decreases linearly, that of BB mode is constant, and that of SB mode increases linearly. The first two order natural frequencies of the rotor and SB mode are both af- fected by the position of the disk and are symmetric around the center of the shaft. The first order natural frequency of SB mode increases gradually during the motion of disk from the end of the shaft to the middle and reaches the maximum in the middle. The second order natural frequency of SB mode first increases and then decreases during the motion of disk from the end of the shaft to the middle and reaches the minimum in the middle. And the changing trend of both kinds of frequencies will be more obvious when the number of blades increases. The change of the natural frequencies of rotor is opposite to than of the SB mode, but the changing trend of frequencies is not affected by the number of blades. The research achievements of the paper have certain guiding significance for the further research of inherent characteristics of the blade-rotor system.