复数坐标及互激励分析在直升机“地面共振”分析中的应用

THE APPLICATION OF COMPLEX COORDINATES AND MUTUAL EXCITATION ANALYSIS TO THE INVESTIGATION OF HELICOPTER GROUND RESONANCE

本文采用复数坐标来表示旋翼及机体的运动,提出了多自由度耦合系统动稳定性问题的各自由度间相互激励作用的分析方法。以此分析了直升机旋翼与机体耦合的“地面共振”稳定性问题,对动不稳定性的机理作出了清晰的物理解释,揭示了主要的参数影响。

The rotor longitudinal and lateral lead-lag motions and the body motion are expected by complex variables. A method to analyze the mutual excitation(work done by one d. o. f on another d. o. f)between different d. o. f quantitativeiy is developed.These two methods are successfully applied to investigating helicopter ground resonance, a kind of rotor/body coupled dynamic instability. The complex eigenvalue and eigenvectors combined together clearly describe the characteristics of the resultant motion. In the case of equal longitudinal and lateral body equivalent mass and spring, the rotor lead-lag motion and body motion are a kind of one-directional whirling motion. In the case of unequal mass and spring, tne resultant motion is a combination of two counter-whirling motions. Instability occurs in a region near the frequency coalescence point of the rotor lead-lag regressive mode and body mode. Tne source of instability is tne positive mutual excitation between regressive lead-lag motion and body forward whirling motion due to inertial coupling. Tne mecnanism of instability and the influences of main factors are revealed through the approximate expressions of mutual excitation and the illustration of blade motion and nub center motion of the unstable mode.The complex coordinate and mutual excitation analysis are proved to be valuable in the investigation of such kinds of multi-d. o. f dynamic systems.