任意斜裂纹转子的耦合振动研究  

STUDY ON COUPLED VIBRATIONS OF ROTOR WITH AN ARBITRARY SLANT CRACK

作　　者：焦卫东[1] 蒋永华[1] 李刚 蔡建程[1] Jiao Weidong;Jiang Yonghua;Li Gang;Cai Jiancheng(School of Engineering,Zhejiang Normal University,Jinhua 321004,Zhejiang,China)

机构地区：[1]浙江师范大学工学院,浙江金华321004

出　　处：《力学学报》2020年第2期533-543,共11页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(51575497)。

摘　　要：对包含不同类型裂纹(横裂纹、横-斜裂纹以及任意斜裂纹)的转子的耦合振动进行研究,以揭示裂纹转子在不同方向上刚度参数的变化规律及其交叉耦合机理,特别是由此引发的振动特征.对于包含不同类型裂纹的转子轴段,采用六自由度Timoshenko梁单元模型对其进行单元建模,并基于应变能理论推导计算柔度参数和刚度矩阵.在此基础上,采用纽马克-β数值算法求解裂纹转子的运动方程,获得裂纹转子在单故障或多故障激励(不平衡激励、扭转激励或不平衡激励加扭转激励)作用下的耦合振动响应,进而分析耦合振动谱特征.与横裂纹和横-斜裂纹相比,任意斜裂纹使转子刚度矩阵的交叉耦合效应更显著,导致转子发生更强烈的弯-扭耦合甚至是纵-弯-扭耦合振动.无论是在不平衡激励还是扭转激励作用下,弯曲振动与扭转振动幅度都更大.而且,包含不同类型裂纹的转子的耦合振动特征频率,例如旋转基频与二倍频、扭转激励频率及其边带成分的幅值,对裂纹面方向角具有不同的敏感性.所得的这些研究结果,可以为转子裂纹的特征参数辨识与诊断提供理论依据.The coupled vibrations of rotor with different type of cracks were studied, including transverse crack, transverseslant crack and arbitrary slant crack. It aims to reveal the variation rule of stiffness parameters in different directions, their cross-coupling mechanism and especially the feature of resulted vibrations of the cracked rotor. The rotor segment with different type of cracks, including transverse crack, transverse-slant crack and arbitrary slant crack, was respectively modeled using the Timoshenko beam element, considering all six degrees of freedom including longitudinal, bending and torsional directions. Flexibility coefficients and then stiffness matrix was derived, based on strain energy theory.On this basis, motion equation of the cracked rotor was solved by numerical algorithm ‘Newmark-beta’ to obtain the time-domain response of coupled vibrations of the cracked rotor under different excitations by single or multiple faults such as unbalanced excitation, torsional excitation and combined excitation of unbalanced with torsional. The spectral characteristics of coupled vibrations were then analyzed. Compared to either transverse crack or transverse-slant crack,the stiffness matrix governed by arbitrary slant crack is more populated with additional cross coupled coefficients, and its cross coupling effect is more significant, which contributes to stronger coupled vibrations in bending-torsional direction or even longitudinal-bending-torsional direction. The amplitudes of both bending vibration and torsional vibration are larger than that at the situation of either transverse crack or transverse-slant crack, under the action of either unbalanced excitation or torsional excitation. Moreover, the characteristic frequencies of coupled vibrations of rotor with different type of cracks including transverse crack, transverse-slant crack and arbitrary slant crack, are of different sensitivities to oriented angle of crack surface, for example the rotating fundamental frequency and its second harmonic fr

关 键 词：任意斜裂纹 变刚度 多故障 耦合振动 转子裂纹诊断 

分 类 号：TH113.1[机械工程—机械设计及理论]