多转子系统振动分析的子结构耦合矩阵法

Substructure coupled matrix method for vibration analysis of multi-rotor systems

提出了一种用于多转子耦合系统振动分析的建模方法.将耦合的多转子系统在耦合处分开,把耦合力作为单转子系统上的外力,利用集总参数法和节点的自由振动微分方程通式建立单转子系统的振动方程.通过分析耦合部件作用在耦合节点上的力,得到了多转子系统耦合部件的耦合矩阵;利用耦合矩阵将单转子系统振动微分方程耦合在一起,建立了整个多转子系统的振动方程.通过分析多转子系统的振动方程,解出了多转子系统的固有频率、临界转速、幅频响应曲线、涡动轨迹等.通过两个算例,证实了多转子系统振动分析的子结构耦合矩阵法是可行的,计算结果是可靠的.

A modeling method was presented to analyze the vibration of a multi-rotor system. The multi rotor system was divided into single-rotor systems at the coupled parts. The coupled forces were regarded as the external exciting forces for each single rotor system. The vibration equations of the single rotor system were derived from the lumped mass method and the vibration equations of each node. The coupled matrixes of the multi rotor system were deduced from the expression of the coupled forces. The global vibration equations of the multi-rotor system were established using the coupled matrixes. The nature frequencies, critical speeds, frequency amplitude diagram and whirling orbit etc. , were obtained by analyzing the global vibration equations of the whole systems. Finally, the feasibility and the reliability of the substructure coupled matrix method for vibration analysis of multi rotor system were proved though two numerical examples.