本文选取含裂纹悬臂梁模拟含裂纹压气机叶片，基于无质量扭转弹簧和呼吸式裂纹刚度模型，得到一种不同环境温度下含裂纹压气机叶片的模态特征和振动特性的分析方法。通过弹性模量引入温度模块，利用无质量扭转弹簧连续条件得到关于含裂纹梁的特征方程，分析环境温度和裂纹深度对含裂纹梁固有频率的影响；利用悬臂梁的强迫弯曲振动方程，引入呼吸式裂纹刚度模型，改变激振力频率，分析环境温度及激振频率对含裂纹梁振动位移响应的影响。结果表明，环境温度越高，含裂纹梁的固有频率越小，梁的振动位移响应越大。同时，激振频率的选取也具有一定影响。
In this paper, a cracked cantilever beam is selected to simulate a cracked compressor blade. Based on a massless torsion spring and a breathing crack stiffness model, a method for analyzing the modal characteristics and vibration characteristics of a cracked compressor blade at different ambient temperatures is obtained. The elastic modulus is introduced into the temperature module, and the characteristic equation about the cracked beam is obtained by using the continuous condition of the massless torsion spring, and the influence of the ambient temperature and crack depth on the natural frequency of the cracked beam is analyzed; the forced bending vibration equation of the cantilever beam is used to introduce the breathing The crack stiffness model was used to change the excitation force frequency to analyze the influence of ambient temperature and excitation frequency on the vibration displacement response of the beam with cracks. The results show that the higher the ambient temperature, the smaller the natural frequency of the beam with cracks, and the greater the vibration displacement response of the beam; at the same time, the selection of the excitation frequency also has a certain influence.
2023,45(12): 93-98 收稿日期：2022-05-07
DOI：10.3404/j.issn.1672-7619.2023.12.017
分类号：TK221
基金项目：国家科技重大专项
作者简介：周震霆(1998-),男,硕士研究生,主要研究方向为动力机械及热力系统的设计、仿真与优化
参考文献：
[1] OSTACHOWICZ W M, KRAWCZUK M. Analysis of the effect of crack on the natural frequencies of a cantilever beam[J]. Journal of Sound and Vibration, 1991, 150(2): 191–201
[2] 王术新, 姜哲. 裂缝悬臂梁的振动特性及其裂缝参数识别[J]. 振动与冲击, 2003, 22(3): 83–85
[3] QIAN G L, GU S. N, JIANG J. S, The dynamic behavior and crack detection of a beam with a crack[J]. Journal of Sound and Vibration, 1990, 138(2): 233-243.
[4] 董广明, 陈进, 邹剑. 裂纹转子的振动特性与裂纹参数识别[J]. 上海交通大学学报, 2004, 38(6): 857–861
[5] CHEN L H, DUAN J W, SUN Y, et al. The study of the vibration characteristics of the cantilever beam with a surface C[J]. Applied Mechanics and Materials, 2013(394): 121–127
[6] 杨海燕, 杨秉玉, 刘启州. 疲劳裂纹叶片振动的非线性特性研究[J]. 西北工业大学学报, 1999, 17(2): 198–204
[7] 胡家顺, 冯新, 周晶. 呼吸裂纹梁非线性动力特性研究[J]. 振动与冲击, 2009, 28(1): 76–80,87
[8] 刘文光, 陈国平. 含裂纹悬臂梁的振动与疲劳耦合分析[J]. 振动与冲击, 2011, 30(5): 140–144
[9] XIE J, ZI Y, ZHANG M, et al. A novel vibration modeling method for a rotating blade with breathing cracks[J]. Science China: Technology Sciences, 2019, 62(2): 333–348
[10] 马一江, 陈国平. 不同温度下裂纹悬臂梁的模态和疲劳寿命分析[J]. 振动与冲击, 2017, 36(8): 132–137+163
[11] 孙强, 张忠平, 柴桥,等. 航空发动机压气机叶片振动频率与温度的关系[J]. 应用力学学报, 2004, 21(4): 137–139
[12] 王振清, 刘兵, 韩玉来. 高温下含裂纹铝合金梁自由振动频率分析[J]. 哈尔滨工程大学学报, 2012, 33(3): 320–324
[13] 中国标准出版社. 中国航空材料手册——钛合金、铜合金[M]. 2001, 2 (3).
[14] 刘文光, 陈国平. 呼吸式裂纹梁的振动疲劳裂纹扩展耦合分析[J]. 中国机械工程, 2010, 21(23): 2798–2802
[15] 辛格雷苏. S. 拉奥. 机械振动[M]. 李欣业, 杨理诚译. 北京: 清华大学出版社, 2016.
