基于哈密尔顿原理和谐波平衡法研究带冠叶片的振动特性  

Study on Vibration Characteristics of Shrouded Blades Based on Hamilton Principle and Harmonic Balance Method

作　　者：王威涛 南国防[1] WANG Weitao;NAN Guofang(Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering,School of Energy and Power Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学能源与动力工程学院,上海市动力工程多相流动与传热重点实验室,上海200093

出　　处：《动力工程学报》2020年第2期117-122,共6页Journal of Chinese Society of Power Engineering

摘　　要：建立自带平行四边形叶冠的等截面直叶片模型来研究系统参数对叶片振动特性的影响,其中直叶片被等效为一个欧拉伯努利梁,叶冠部分被视为一个与叶顶固连的集中质量,叶冠之间碰撞的接触力则引入弹簧模型来定义。根据哈密尔顿原理推导出系统动力学方程,再采用谐波平衡法将叶冠间的压力和摩擦力转换为等效刚度和等效阻尼,得到汽轮机自带冠叶片等效后的动力学方程,通过龙格库塔法求解系统的振动响应,探讨了叶冠间隙、叶冠间摩擦因数和接触角对振动特性的影响以及系统相关非线性行为。结果表明:振幅在一定范围内随着叶冠间隙的增加而增大,而叶冠间隙对发生共振时的转速几乎没有影响;摩擦因数增大会导致振幅和共振区域减小;存在一个最佳接触角,可使减振效果处于最佳状态;叶片在有摩擦存在时的振动相对稳定。A dynamic model was established for the straight blade with parallelogram shroud to study the influence of different parameters on the vibration characteristics of the blade,during which,the straight blade was simplified as a cantilever Euler-Bernoulli beam,the shroud was seemed as a mass concentration point fixing with the blade tip,and the contact force between shrouded blades was defined using a spring model.A dynamic equation of the system was deduced based on Hamilton principle,while an equivalent dynamic equation of the blade with shroud was obtained by translating the compressive stress and friction force between the shrouds into equivalent stiffness and equivalent damping using harmonic balance method.The dynamic response of the system was then acquired by solving above equations using Runge-Kutta numerical method to find out how the gap of tip,the rub coefficient and the contact angle influence the vibration characteristics and the nonlinear behaviors of the model proposed.Results show that the resonance amplitude increases with the rise of the shroud gap in a certain range,while the gap has nearly no effects on the rotating speed in case of resonance.The resonance amplitude and range reduce with the increase of rub coefficient.There exists an optimal contact angle,when best damping effectiveness could be obtained.The vibration of blade is relatively stable under friction conditions.

关 键 词：带冠叶片 非线性振动 摩擦力 谐波平衡法 

分 类 号：TK263.3[动力工程及工程热物理—动力机械及工程]