转子运动激励下叶片的振动特性分析  

Analysis of Vibration Characteristics of Blade under Rotor Motion

作　　者：武立明[1,2,3] 曹树谦 WU Liming;CAO Shuqian(Department of Mechanics,Tianjin University,Tianjin 300354;Tianjin Key Laboratory of Nonlinear Dynamics and Control,Tianjin 300354;National Demonstration Center for Experimental Mechanics Education(Tianjin University),Tianjin 300354)

机构地区：[1]天津大学力学系,天津300354 [2]天津市非线性动力学与控制重点实验室,天津300354 [3]力学国家级实验教学示范中心(天津大学),天津300354

出　　处：《机械工程学报》2019年第19期92-102,共11页Journal of Mechanical Engineering

基　　金：国家重点基础研究发展计划(2015CB057400);国家自然科学基金(11672201,11872045);国家科技重大专项(2017-IV-0008-0045)资助项目

摘　　要：研究了航空发动机叶片在转子运动激励下的非线性动力学特性,利用一阶活塞理论来计算气动力,考虑大变形所带来的几何非线性的影响,利用Hamilton原理建立了叶片的连续体模型,采用伽辽金法将叶片简化为单自由度模型,通过多尺度法导出了叶片在参数激励与强迫激励作用下联合共振幅频响应的一阶近似方程;分析了转子扭转角度的幅值、稳定转速、气体的来流速度以及叶片的形状参数对于叶片幅频响应特性的影响。通过解析和数值分析,表明以上的参数是促使叶片动力学行为发生变化的敏感参数。同时应用奇异性理论得到系统主参数共振-主共振稳态响应的转迁集和分岔图,并对低风速情况下的叶片进行了试验分析。The nonlinear dynamic characteristics of aero engine blades under rotor excitation are studied. Using the large deflection nonlinear relation and the first order piston theory of supersonic flow, the continuum model of blade is established by using Hamilton principle and simplified to a single degree of freedom model by Galerkin method. The first order approximate equation for resonance amplitude frequency response of blades under the combined action of parametric excitation and forced excitation is derived by means of multi-scale method. The influence of the amplitude of the torsional angle, the steady speed of the rotor, the velocity of gas flow and the shape parameters of the blade on the amplitude-frequency response characteristics of the blade are analysed. Through analytical and numerical analyses, it is shown that the presented parameters are sensitive parameters for the dynamical properties of blades. At the same time, by using the singularity theory, the transition set and bifurcation diagram of the principal parametric resonance-primary resonance steady-state response of the system are obtained, and the experimental analysis of the blades under low flow velocity is carried out.

关 键 词：航空发动机叶片 多尺度法 联合共振 奇异性理论 

分 类 号：TH113[机械工程—机械设计及理论]