摘 要：将自带冠叶片模化为质量弹簧模型。自带冠叶片减振主要是由于冠间碰撞和摩擦的组合运动来实现的，因此本文将冠间的接触简化为带对称间隙的弹簧阻尼模型，摩擦模型采用Sgn模型，从而建立该系统的动力学方程，进而采用Runge-Kutta数值方法求解系统的动力学方程。本文主要探讨了冠间间隙、刚度比、接触角度、摩擦系数等多种参数对减振效果的影响。结果表明：叶片的振动能量与冠间间隙、刚度比、接触角度、摩擦系数等参数有关，参数选取要考虑工作转速的范围。冠间的碰摩组合运动为硬式分段线性的非线性振动，因此本文同时采用Poincaré映射图和频谱图等方法对系统的非线性特性进行了一定的研究。

Abstract: The blade with tips can be equivalent to the model of mass with springs in this paper. It is achieved for the blade with tips to be damping by means of the multiple motions of impact and friction between the blades with tips, so in the paper, the friction between blades with tips can be equivalent to the spring and damping model with symmetry gap. Sgn contact model is used, thus the paper gets the dynamical equation of the system, and solves the equation by Runge-Kutta numerical method. The paper mainly discusses how the parameters such as gap of tips, stiffness ratio, contact angle, friction coefficient make impact on damping effect. The result shows that the parameters make an important impact on vibration energy, selecting parameter is subjected to span of rotate speed. The multiple motions of impact and friction between the blades with tips is hard piecewise linear vibration which is actually nonlinear, so the paper also makes certain research on the nonlinear characteristic of the system by means of Poincaré graph and frequency spectrum etc.