转轴-轮盘-裂纹叶片耦合系统的叶尖振动特性

Vibration characteristics of blade tip in a shaft⁃disk⁃cracked⁃blade coupling system

航空发动机叶片在极端恶劣环境中工作,容易产生裂纹进而缩短叶片寿命,严重影响航空发动机的安全运行。以转轴-轮盘-裂纹叶片耦合系统为研究对象,采用有限元、假设模态混合的建模策略,利用有限元模拟转轴,基于Kirch⁃hoff板理论、Timoshenko梁理论模拟轮盘、旋转叶片,并根据时变的释放应变能确定呼吸裂纹导致的时变损失刚度,建立了相应的动力学模型;通过对比耦合系统的固有特性和振动响应验证了提出方法的正确性;剖析了重力载荷、转子不平衡力、气动载荷对叶尖振动特性的影响,并研究了不同无量纲裂纹深度和裂纹位置对叶尖振动特性的影响。研究结果表明:健康叶片中,重力载荷会导致叶片产生振动,转子不平衡力会导致叶片发生静变形;在旋转状态下,裂纹叶片导致叶尖弯曲位移产生偏移量;在气动载荷作用下,呼吸裂纹导致叶片发生非线性振动;常值分量与转频幅值比、常值分量与气动激励频率幅值比是评价呼吸裂纹的有效指标。本文的建模方法和分析结论可为航空发动机叶片裂纹故障诊断提供了一定的理论依据。

Aero-engine blades,subjected to extreme environmental conditions,are susceptible to crack develop⁃ment,which shortens blade life and seriously affects the safe operation of aero-engine.This paper focuses on the shaft-disk-cracked-blade coupling system which is modeled using the mixed strategy of the finite element method and the assumed mode method.The shaft is simulated by finite element method,while the disk and blade are simulated by Kirchhoff plate theory and Timoshenko beam theory.A dynamic model is built based on time-varying loss stiffness caused by the breathing crack which is determined by the time-varying release strain energy.The correctness of the proposed method is confirmed by comparing the natural characteristics and vibration responses of the coupling sys⁃tem.The influences of gravity load,rotor unbalance force and aerodynamic load on vibration characteristics of the blade tip are analyzed,and the impact of different dimensionless crack depths and crack locations on the vibration characteristics of the blade tip are investigated.The research results show that:in a healthy blade,the gravity load can cause the blade to vibrate,and the unbalanced force can induce the static deformation of the blade;under rota⁃tion,the cracked blade leads to the bending displacement of the blade tip,which produces an offset,while under the action of aerodynamic load,the breathing crack results in nonlinear vibration of the blade;the amplitude ratio of the constant component to the rotational frequency and the amplitude ratio of the constant component to the aerodynamic excitation frequency are valuable indicators for assessing breathing crack.The modeling method and analysis conclu⁃sions in this paper can provide a specific theoretical basis for the fault diagnosis of aero-engine blade crack.