空间任意斜裂纹引起的转子刚度变化机理研究
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摘要
转子在不同方向上刚度的变化特性及其交叉耦合是导致转子耦合振动的根本原因。基于材料力学和断裂力学理论,采用六自由度Timoshenko梁单元模型推导了空间任意斜裂纹的柔度参数和刚度矩阵,据此对比分析了含有横裂纹、横-斜裂纹以及空间任意斜裂纹转子因为旋转过程中的裂纹非线性呼吸(开/合)行为所导致的变刚度特性。与横裂纹与横-斜裂纹相比,空间任意斜裂纹的刚度矩阵具有更加广泛、更加明显的外加交叉耦合项。此外,针对空间任意斜裂纹情况,系统研究了裂纹方位角以及裂纹深度等参数对转子刚度特性的影响。所得的研究结果可以为进一步研究裂纹转子的耦合振动行为以及诊断应用奠定基础。
Stiffness variation characteristics of rotor in different directions and their cross coupling is the fundamental cause for its coupled vibration.Based on the theories of material mechanics and fracture mechanics,the flexibility coefficients and then the stiffness matrix for the Timoshenko beam element with an arbitrary spatial slant crack is derived,considering all the six degrees of freedom.Comparison among rotor with transverse,transverse-slant and arbitrary slant crack is made with regard to the stiffness variation characteristics due to nonlinear breathing behavior during rotation.Compared to either transverse or transverse-slant crack,the stiffness matrix for arbitrary spatial slant crack is more popular with additional cross coupling coefficients.In addition,the influence of both the oriented angle and the depth of the arbitrary spatial slant crack on the stiffness values is also investigated.The comparison results of different types of crack may be served as the theoretical foundation for the further study of the coupled vibration and diagnostics for rotors.
Stiffness variation characteristics of rotor in different directions and their cross coupling is the fundamental cause for its coupled vibration.Based on the theories of material mechanics and fracture mechanics,the flexibility coefficients and then the stiffness matrix for the Timoshenko beam element with an arbitrary spatial slant crack is derived,considering all the six degrees of freedom.Comparison among rotor with transverse,transverse-slant and arbitrary slant crack is made with regard to the stiffness variation characteristics due to nonlinear breathing behavior during rotation.Compared to either transverse or transverse-slant crack,the stiffness matrix for arbitrary spatial slant crack is more popular with additional cross coupling coefficients.In addition,the influence of both the oriented angle and the depth of the arbitrary spatial slant crack on the stiffness values is also investigated.The comparison results of different types of crack may be served as the theoretical foundation for the further study of the coupled vibration and diagnostics for rotors.
引文
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[11]夏恒恒,李志农,肖尧先.斜裂纹转子全开状态的刚度影响因素分析[J].南昌航空大学学报(自然科学版),2014,28(3):22—28.Xia Heng-heng,Li Zhi-nong,Xiao Yao-xian.Stiffness influencing factors analysis of the fully opened slant crack rotor[J].Journal of Nanchang Hangkong University(Natural Science),2014,28(3):22—28.
[12]孙训方,方孝淑,陆耀洪.材料力学[M].第3版.北京:高等教育出版社,2012:152—161.Sun Xun-fang,Fang Xiao-shu,Lu Yao-hong.Mechanics of Materials[M].3rd ed.Beijing:Higher Education Press,2012:152—161.
[2]Chen Y S,Zhang H B.Review and prospect on the research of dynamics of complete aero-engine systems[J].Acta Aeronautica et Astronautica Sinica,2011,32(8):1371—1391.
[3]Darpe A K,Gupta K,Chawla A.Coupled bending,longitudinal and torsional vibrations of a cracked rotor[J].Journal of Sound and Vibration,2004,269(1):33—60.
[4]Darpe A K.Coupled vibrations of a rotor with slant crack[J].Journal of Sound and Vibration,2007,305(1-2):172—193.
[5]Bachschmid N,Pennacchi P,Tanzi E.Some remarks on breathing mechanism,on non-linear effects and on slant and helicoidal cracks[J].Mechanical Systems and Signal Processing,2008,22(4):879—904.
[6]Han Q K,Zhao J S,Chu F L.Dynamic analysis of a geared rotor system considering a slant crack on the shaft[J].Journal of Sound and Vibration,2012,331(26):5803—5823.
[7]Ebrahimi A,Heydarin M,Behzad M.A continuous vibration theory for rotors with an open edge crack[J].Journal of Sound and Vibration,2014,333(15):3522—3535.
[8]闫明,张义民,何雪浤,等.热疲劳斜裂纹应力强度因子有限元分析[J].东北大学学报(自然科学版),2011,32(5):720—723.Run Ming,Zhang Yi-min,He Xue-hong,et al.Timevarying stiffness characteristics of rotating shaft with transverse and slant crack[J].Journal of Northeastern University(Natural Science),2011,32(5):720—723.
[9]刘长利,李诚,周邵萍,等.直斜裂纹转轴的时变刚度特性研究[J].振动与冲击,2011,30(3):165—170.Liu Chang-li,Li Cheng,Zhou Shao-ping,et al.Timevarying stiffness characteristics of rotating shaft with transverse and slant crack[J].Journal of Vibration and Shock,2011,30(3):165—170.
[10]刘长利,周邵萍,江君,等.双盘双呼吸型裂纹转子的非线性动力学特性[J].振动、测试与诊断,2012,32(S1):136—140.Liu Chang-li,Zhou Shao-ping,Jiang Jun,et al.Nonlinear dynamics analysis of double-disc rotor with two breathing cracks[J].Journal of Vibration,Measurement&Diagnosis,2012,32(S1):136—140.
[11]夏恒恒,李志农,肖尧先.斜裂纹转子全开状态的刚度影响因素分析[J].南昌航空大学学报(自然科学版),2014,28(3):22—28.Xia Heng-heng,Li Zhi-nong,Xiao Yao-xian.Stiffness influencing factors analysis of the fully opened slant crack rotor[J].Journal of Nanchang Hangkong University(Natural Science),2014,28(3):22—28.
[12]孙训方,方孝淑,陆耀洪.材料力学[M].第3版.北京:高等教育出版社,2012:152—161.Sun Xun-fang,Fang Xiao-shu,Lu Yao-hong.Mechanics of Materials[M].3rd ed.Beijing:Higher Education Press,2012:152—161.